http://www.cfd-online.com/W/index.php?title=Special:Contributions/Zxaar&feed=atom&limit=50&target=Zxaar&year=&month=CFD-Wiki - User contributions [en]2016-09-29T21:15:37ZFrom CFD-WikiMediaWiki 1.16.5http://www.cfd-online.com/Wiki/CodesCodes2011-05-06T09:29:16Z<p>Zxaar: </p>
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<div>An overview of both free and commercial CFD software. Here you will find short descriptions of codes along with links to resources.<br />
<br />
'''Note to contributers:''' Please try to keep descriptions short and to the point (approximately 200 words) and avoid long lists of features or capabilities. Also keep in mind that all contributions are considered to be released under the GNU Free Documentation License 1.2 (see [[Project:Copyrights]] for details). Also note that all information should be verifiable and objective truths that also competitors to the code in question will agree upon. This is especially important if you are an employee of the company selling the code. See the [[CFD-Wiki:Policy]] for further information.<br />
<br />
== Free codes ==<br />
<br />
This section lists codes that are in the public domain, and codes that are available under GPL, BSD or similar licenses.<br />
<br />
=== Solvers ===<br />
* ADFC -- [http://adfc.sourceforge.net/index.html ADFC homepage]<br />
* Applied Computational Fluid Dynamics -- [http://www.partenovcfd.com Solver homepage]<br />
* CFD2k -- [http://www.cfd2k.eu/ CFD2k: a 2D-solver for compressible ideal gases - homepage]<br />
* Channelflow -- [http://www.cns.gatech.edu/channelflow/ Channelflow: a spectral Navier-Stokes simulator in C++ homepage]<br />
* CLAWPACK -- [http://www.amath.washington.edu/~claw/clawpack.org CLAWPACK homepage]<br />
* Code_Saturne -- [http://www.code-saturne.org/ Code_Saturne homepage]<br />
* COOLFluiD -- [http://coolfluidsrv.vki.ac.be/coolfluid COOLFluiD homepage]<br />
* Diagonalized Upwind Navier Stokes -- [http://duns.sourceforge.net DUNS homepage]<br />
* [[Dolfyn]] -- [http://www.dolfyn.net/dolfyn/index_en.html dolfyn a 3D unstructured general purpose solver - homepage]<br />
*[[Edge]] -- [http://www.foi.se/edge Edge homepage: 2D & 3D compressible RANS / Euler flow solver on unstructured and hybrid grids]<br />
*[[ELMER]] -- [http://www.csc.fi/elmer/ ELMER homepage]<br />
* [[FDS]] -- [http://www.fire.nist.gov/fds/ FDS homepage]<br />
* Featflow -- [http://www.featflow.de Featflow homepage]<br />
* Femwater -- [http://www.epa.gov/ceampubl/gwater/femwater/index.htm Femwater code]<br />
* FreeFEM -- [http://www.freefem.org FreeFEM homepage]<br />
*[[Gerris Flow Solver]] -- [http://gfs.sourceforge.net/ Gerris Flow Solver homepage]<br />
* [[GPDE]] -- [http://www.gpde.net Discrete adjoint flow field computation | 2/3D FV, unstr, incomp, F90]<br />
* IMTEK Mathematica Supplement (IMS) -- [http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/ IMTEK Mathematica Supplement (IMS) homepage]<br />
* iNavier -- [http://inavier.com/ iNavier Solver Home Page]<br />
* ISAAC -- [http://isaac-cfd.sourceforge.net ISAAC Home Page]<br />
* Kicksey-Winsey -- [http://justpmf.com/romain/kicksey_winsey/ Kicksey-Winsey Home Page]<br />
* MFIX -- [https://mfix.netl.doe.gov Computational multiphase flow homepage]<br />
*[[NaSt2D-2.0]] -- [http://home.arcor.de/drklaus.bauerfeind/nast/eNaSt2DA.html NaSt2D-2.0 homepage]<br />
*[[NEK5000]] -- [http://nek5000.mcs.anl.gov NEK5000 homepage]<br />
*[[NSC2KE]] -- [http://www-rocq1.inria.fr/gamma/cdrom/www/nsc2ke/eng.htm NSC2KE homepage]<br />
* NUWTUN -- [http://nuwtun.berlios.de NUWTUN Home Page]<br />
*[[OpenFlower]] -- [http://sourceforge.net/projects/openflower/ OpenFlower homepage]<br />
*[[OpenFOAM]] -- [http://www.openfoam.org/ OpenFOAM homepage]<br />
*[[OpenLB]] -- [http://www.openlb.net/ OpenLB homepage]<br />
* OpenFVM -- [http://openfvm.sourceforge.net/ OpenFVM homepage]<br />
* PETSc-FEM -- [http://www.cimec.org.ar/petscfem PETSc-FEM homepage]<br />
* PP3D -- [http://www.featflow.de/ parpp3d++ homepage]<br />
* REEF3D -- [http://www.reef3d.com REEF3D homepage]<br />
* SLFCFD -- [http://slfcfd.sourceforge.net SLFCFD homepage]<br />
*[[SSIIM]] -- [http://folk.ntnu.no/nilsol/cfd/ CFD at NTNU]<br />
*[[Tochnog]] -- [http://tochnog.sourceforge.net Tochnog homepage]<br />
* Typhon solver -- [http://typhon.sf.net Typhon solver homepage]<br />
<br />
=== Grid generation ===<br />
*[[Delaundo]] -- [http://www.cerfacs.fr/~muller/delaundo.html Delaundo homepage]<br />
* GMSH -- [http://www.geuz.org/gmsh/ GMSH hompage]<br />
* NETGEN -- [http://www.hpfem.jku.at/netgen/ NETGEN homepage]<br />
* SALOME -- [http://www.salome-platform.org SALOME homepage]<br />
* TETGEN -- [http://tetgen.berlios.de/ TETGEN hompage]<br />
*[[Triangle]] -- [http://www.cs.cmu.edu/~quake/triangle.html Triangle homepage]<br />
* gridgen -- [http://code.google.com/p/gridgen-c gridgen homepage]<br />
* IA-FEMesh -- [http://www.ccad.uiowa.edu/mimx/IA-FEMesh IA-FEMesh homepage]<br />
* Engrid -- [http://engrid.sourceforge.net Engrid homepage]<br />
<br />
=== Visualization ===<br />
*[[DISLIN]] -- [http://www.mps.mpg.de/dislin/server.html DISLIN homepage]<br />
* GMV -- [http://www-xdiv.lanl.gov/XCM/gmv/ GMV homepage]<br />
*[[Gnuplot]] -- [http://www.gnuplot.info/ gnuplot homepage]<br />
* GRI -- [http://gri.sourceforge.net/ GRI homepage]<br />
*[[Mayavi]] -- [http://mayavi.sourceforge.net/ MayaVi homepage]<br />
*[[OpenDX]] -- [http://www.opendx.org OpenDX homepage]<br />
*[[ParaView]] -- [http://www.paraview.org/HTML/Index.html ParaView homepage]<br />
*[[Tioga]] -- [http://www.kitp.ucsb.edu/~paxton/tioga.html Tioga homepage]<br />
*[[VAPOR]] -- [http://www.vapor.ucar.edu VAPOR homepage]<br />
*[[Vigie]] -- [http://www-sop.inria.fr/sinus/Softs/vigie.html Vigie homepage]<br />
*[[Visit]] -- [http://www.llnl.gov/visit Visit homepage]<br />
*[[vtk]] -- [http://www.vtk.org vtk homepage]<br />
*[[vtk.Net]] -- [http://vtkdotnet.sourceforge.net/ vtk.Net homepage] <br />
<br />
=== Miscellaneous ===<br />
<br />
*[[Engauge Digitizer]] -- [http://digitizer.sourceforge.net Engauge Digitizer homepage]<br />
*[[Ftnchek]] -- [http://www.dsm.fordham.edu/~ftnchek/ ftnchek homepage]<br />
*[[g3data]] -- [http://www.frantz.fi/software/g3data.php g3data homepage]<br />
* GIFMerge -- [http://www.the-labs.com/GIFMerge/ GIFMerge homepage]<br />
*[[Gifsicle]] -- [http://www.lcdf.org/~eddietwo/gifsicle/ Gifsicle homepage]<br />
*[[ImageMagick]] -- [http://www.imagemagick.org ImageMagick homepage]<br />
* nnbathy (natural neighbor interpolation) -- [http://code.google.com/p/nn-c/ nnbathy home page]<br />
*[[O-PALM]] -- [http://www.cerfacs.fr/globc/PALM_WEB O-PALM homepage]<br />
* [[OpenGPI]] (Generic Parameter Interface) -- [http://www.opengpi.org OpenGPI homepage]<br />
<br />
== Commercial codes ==<br />
<br />
=== Solvers ===<br />
* 6sigmaDC -- [http://www.futurefacilities.com Future Facilities homepage]<br />
* EasyCFD -- [http://www.easycfd.net EasyCFD homepage]<br />
* Applied Computational Fluid Dynamics -- [http://www.partenovcfd.com Solver homepage]<br />
* AcuSolve -- [http://www.acusim.com/ ACUSIM Software's homepage]<br />
* ADINA-F -- [http://www.adina.com/index.html ADINA's homepage]<br />
* ADINA-FSI -- [http://www.adina.com/index.html ADINA's homepage]<br />
* ANSWER -- [http://www.acricfd.com/ ACRi's homepage]<br />
*[http://www.cfd-online.com/W/index.php?title=CFD%2B%2B CFD++] -- [http://www.metacomptech.com Metacomp Techonlogies' homepage]<br />
* CFD2000 -- [http://www.adaptive-research.com/ Adaptive Research's homepage]<br />
*[[CFD-FASTRAN]] -- [http://www.esi-group.com/SimulationSoftware/advanced.html ESI Group's homepage]<br />
* CFD-ACE -- [http://www.esi-group.com/SimulationSoftware/advanced.html ESI Group's homepage]<br />
* CFdesign -- [http://www.cfdesign.com CFdesign's homepage]<br />
* CFX -- [http://www.ansys.com/ ANSYS homepage]<br />
* Coolit -- [http://www.daat.com/ Daat Research's Coolit homepage]<br />
* CoolitPCB -- [http://www.coolitpcb.com/ Daat Research's CoolitPCB homepage]<br />
* DLR - TAU -- [http://tau.dlr.de/ TAU's homepage]<br />
* DQMoM -- [http://www.cmclinnovations.com/userstories/userstory9.html cmcl innovations' product page]<br />
*[[FENSAP-ICE]] -- [http://www.newmerical.com/ NTI' homepage]<br />
* FINE/Hexa -- [http://www.numeca.be/ Numeca's homepage]<br />
* FINE/Turbo -- [http://www.numeca.be/ Numeca's homepage]<br />
* FIRE -- [http://www.avl.com/ AVL's homepage]<br />
*[[FLACS]] -- [http://www.gexcon.com/index.php?src=flacs/overview.html GexCon's homepage]<br />
* COMSOL Multiphysics -- [http://www.comsol.com/ COMSOL's homepage]<br />
* COMSOL Multiphysics CFD Module -- [http://www.comsol.com/products/cfd/ COMSOL's CFD Module]<br />
* FloEFD -- [http://www.mentor.com/products/mechanical/products/floefd Mentor's FloEFD homepage]<br />
* FloTHERM-- [http://www.mentor.com/products/mechanical/products/flotherm Mentor's FloTHERM homepage]<br />
* FloVENT-- [http://www.mentor.com/products/mechanical/products/flovent Mentor's FloVENT homepage]<br />
* FLOW-3D -- [http://www.flow3d.com/ Flow Science's homepage]<br />
* FLOWVISION -- [http://www.fv-tech.com FlowVision's homepage]<br />
*[[FLUENT]] -- [http://www.fluent.com Fluent's homepage]<br />
* [[FLUIDYN]] -- [http://www.fluidyn.com Fluidyn's homepage]<br />
* FluSol -- [http://www.cfd-rocket.com FluSol's hompage]<br />
* Flowz--[http://www.zeusnumerix.com Zeus Numerix's homepage ]<br />
* GASP-- [http://www.aerosoftinc.com AeroSoft homepage]<br />
*[[J-FLO]] -- [http://www.newmerical.com NTI's homepage]<br />
* Kameleon FireEx - KFX -- [http://www.computit.com ComputIT's homepage]<br />
* KINetics Reactive Flows -- [http://www.ReactionDesign.com Reaction Design's homepage]<br />
* KIVA--[http://www.lanl.gov/orgs/t/t3/codes/kiva.shtml Los Alamos homepage]<br />
*[[NOGRID FPM]] -- [http://www.no-grid.com NOGRIDS's homepage]<br />
* NX Electronic Systems Cooling -- [http://www.mayahtt.com/index.php?option=com_content&task=view&id=69&Itemid=237 MAYA's NX ESC page]<br />
* NX Advanced Flow -- [http://www.mayahtt.com/index.php?option=com_content&task=view&id=1&Itemid=115 MAYA HTT's NX Adv. Flow page]<br />
* NX Flow -- [http://www.mayahtt.com/index.php?option=com_content&task=view&id=2&Itemid=116 MAYA HTT's NX Flow page]<br />
* MicroFlo -- [http://www.iesve.com/Software/VE-Pro/MicroFlo homepage]<br />
*[[PHOENICS]] -- [http://www.cham.co.uk CHAM's homepage]<br />
* PowerFLOW -- [http://www.exa.com/pages/pflow/pflow_main.html Exa PowerFLOW homepage]<br />
* PumpLinx -- [http://www.simerics.com Simerics' homepage]<br />
* Range Software -- [http://www.range-software.com Range' homepage]<br />
*[[RheoChart]] -- [http://www.rheochart.com RheoChart Homepage]<br />
* [[Siemens PLM Software CFD]] -- [http://www.plm.automation.siemens.com/en_us/products/nx/simulation/advanced/index.shtml Siemens PLM Software NX CAE page]<br />
*[[Smartfire]] -- [http://fseg.gre.ac.uk/smartfire Smartfire Homepage]<br />
* [[Solution of Boltzmann Equation]] -- [http://www.elegant-mathematics.com/ Elegant Mathematics homepage]<br />
*[[SPLASH]] -- [http://www.panix.com/~brosen SPLASH's homepage]<br />
*[[srm suite]] -- [http://www.cmclinnovations.com/products/srmsuite cmcl innovations' product page]<br />
* STALLION 3D -- [http://www.hanleyinnovations.com/stallion3d.html Hanley Innovations' STALLION 3D homepage]<br />
*[[STAR-CD]] -- [http://www.cd-adapco.com CD-adapco's homepage]<br />
*[[STAR-CCM+]] -- [http://www.cd-adapco.com CD-adapco's homepage]<br />
*[[Tdyn]] -- [http://www.compassis.com CompassIS' homepage]<br />
* TMG-Flow -- [http://www.mayahtt.com/index.php?option=com_content&task=view&id=82&Itemid=283 MAYA HTT's CFD page]<br />
* Turb'Flow -- [http://www.fluorem.com Fluorem's hompage]<br />
* TURBOcfd -- [http://adtechnology.co.uk/products/turbocfd/ TURBOcfd's hompage]<br />
<br />
=== Grid generation ===<br />
<br />
* ADINA-AUI -- [http://www.adina.com/index.html ADINA's homepage]<br />
* AutoMesh4G -- [http://www.numeca.be/ Numeca's homepage]<br />
* Centaur -- [http://www.centaursoft.com CentaurSoft homepage]<br />
*[[CFD-GEOM]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFD-VISCART]] -- [http://www.esi-group.com/ ESI's homepage]<br />
* CFDExpert-GridZ --[http://www.zeusnumerix.com/ Zeus Numerix's homepage]<br />
*[[Gridgen]] -- [http://www.pointwise.com/ Pointwise's homepage]<br />
*[[ GridPro]] -- [http://www.gridpro.com/ PDC's homepage]<br />
* Harpoon -- [http://www.sharc.co.uk/ Harpoon's homepage]<br />
* ICEM CFD -- [http://www.ansys.com/ ANSYS' homepage]<br />
* +ScanFE -- [http://www.simpleware.com/ Simpleware's homepage]<br />
* ANSA -- [http://www.beta-cae.gr/ BETA-CAE's homepage]<br />
* SolidMesh -- [http://www.simcenter.msstate.edu/docs/solidmesh/ SolidMesh homepage]<br />
*[[RBF Morph]] -- [http://www.rbf-morph.com/ RBF Morph homepage]<br />
<br />
=== Visualization ===<br />
<br />
* ADINA-AUI -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[CFD-VIEW]] -- [http://www.esi-group.com/ ESI's homepage]<br />
* CFView -- [http://www.numeca.be/ Numeca's homepage]<br />
* CFX-Post -- [http://www.ansys.com/ ANSYS' homepage]<br />
* COMSOL -- [http://www.comsol.com/ COMSOL's homepage]<br />
* CoolPlot -- [http://www.daat.com/ Daat Research's homepage]<br />
* COVISE -- [http://www.visenso.de/ Visenso's homepage]<br />
* EnSight -- [http://www.ensight.com/ CEI's homepage]<br />
* Fieldview -- [http://www.ilight.com/ Intelligent Light's homepage]<br />
*[[Tecplot]] -- [http://www.tecplot.com/ Tecplot's homepage]<br />
* VU -- [http://www.invisu.ca/ inVisu's homepage]<br />
*ViewZ -- [http://www.zeusnumerix.com/ Zeus Numerix's homepage]<br />
* CFDsoft Viewer -- [http://www.cfdsoft.com/ CFDsoft Viewer homepage]<br />
<br />
=== Systems ===<br />
<br />
* ADINA -- [http://www.adina.com/index.html ADINA's homepage]<br />
* FINE/Design3D -- [http://www.numeca.be/ Numeca's homepage]<br />
* Flowmaster -- [http://www.flowmaster.com/index.html Flowmaster's homepage]<br />
* Flownex -- [http://www.flownex.com/ Flownex's homepage]</div>Zxaarhttp://www.cfd-online.com/Wiki/User:ZxaarUser:Zxaar2007-03-01T22:55:37Z<p>Zxaar: </p>
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<div>I am working in aerodynamics field.<br><br />
I am graduate from IIT-Delhi in chemical engineering field. <br><br />
web: inavier.sourceforge.net</div>Zxaarhttp://www.cfd-online.com/Wiki/CodesCodes2007-02-24T01:09:03Z<p>Zxaar: /* Solvers */</p>
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<div>An overview of both free and commercial CFD software.<br />
<br />
== Free codes ==<br />
<br />
This section lists codes that are in the public domain, and codes that are available under GPL, BSD or similar licenses.<br />
<br />
=== Solvers ===<br />
<br />
*[[ADFC]] -- [http://adfc.sourceforge.net/index.html ADFC homepage]<br />
*[[Diagonalized Upwind Navier Stokes]] -- [http://duns.sourceforge.net DUNS homepage]<br />
*[[Dolfyn]] -- [http://www.dolfyn.net/dolfyn/index_en.html dolfyn homepage]<br />
*[[Edge]] -- [http://www.edge.foi.se/ Edge homepage]<br />
*[[ELMER]] -- [http://www.csc.fi/elmer/ ELMER homepage]<br />
*[[FreeFEM]] -- [http://www.freefem.org FreeFEM homepage]<br />
*[[Gerris Flow Solver]] -- [http://gfs.sourceforge.net/ Gerris Flow Solver homepage]<br />
*[[IMTEK Mathematica Supplement (IMS)]] -- [http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/ IMTEK Mathematica Supplement (IMS) homepage]<br />
*[[iNavier]] -- [http://inavier.sourceforge.net/ iNavier Solver Home Page]<br />
*[[MFIX]] -- [http://www.mfix.org Computational multiphase flow homepage]<br />
*[[NaSt2D-2.0]] -- [http://home.arcor.de/drklaus.bauerfeind/nast/eNaSt2D.html NaSt2D-2.0 homepage]<br />
*[[NSC2KE]] -- [http://www-rocq1.inria.fr/gamma/cdrom/www/nsc2ke/eng.htm NSC2KE homepage]<br />
*[[OpenFlower]] -- [http://sourceforge.net/projects/openflower/ OpenFlower homepage]<br />
*[[OpenFOAM]] -- [http://www.openfoam.org/ OpenFOAM homepage]<br />
*[[OpenFVM]] -- [http://openfvm.sourceforge.net/ OpenFVM homepage]<br />
*[[PETSc-FEM]] -- [http://www.cimec.org.ar/petscfem PETSc-FEM homepage]<br />
*[[PP3D]] -- [http://www.featflow.de/ parpp3d++ homepage]<br />
*[[SLFCFD]] -- [http://slfcfd.sourceforge.net SLFCFD homepage]<br />
*[[Tochnog]] -- [http://tochnog.sourceforge.net Tochnog homepage]<br />
*[[Typhon solver]] -- [http://typhon.sf.net Typhon solver homepage]<br />
<br />
=== Grid generation ===<br />
<br />
*[[Delaundo]] -- [http://www.cerfacs.fr/~muller/delaundo.html Dalaundo homepage]<br />
*[[GMSH]] -- [http://www.geuz.org/gmsh/ GMSH hompage]<br />
*[[NETGEN]] -- [http://www.hpfem.jku.at/netgen/ NETGEN homepage]<br />
*[[SALOME]] -- [http://www.salome-platform.org SALOME homepage]<br />
*[[TETGEN]] -- [http://tetgen.berlios.de/ TETGEN hompage]<br />
*[[Triangle]] -- [http://www.cs.cmu.edu/~quake/triangle.html Trangle homepage]<br />
<br />
=== Visualization ===<br />
<br />
*[[GMV]] -- [http://www-xdiv.lanl.gov/XCM/gmv/ GMV homepage]<br />
*[[Gnuplot]] -- [http://www.gnuplot.info/ gnuplot homepage]<br />
*[[Mayavi]] -- [http://mayavi.sourceforge.net/ MayaVi homepage]<br />
*[[OpenDX]] <br />
*[[ParaView]] -- [http://www.paraview.org/HTML/Index.html ParaView homepage]<br />
*[[Vigie]] -- [http://www-sop.inria.fr/sinus/Softs/vigie.html Vigie homepage]<br />
*[[Visit]]<br />
*[[vtk]] -- [http://www.vtk.org vtk homepage]<br />
*[[vtk.Net]] -- [http://vtkdotnet.sourceforge.net/ vtk.Net homepage]<br />
<br />
=== Miscellaneous ===<br />
<br />
*[[Engauge Digitizer]]<br />
*[[Ftnchek]]<br />
*[[g3data]] -- [http://www.frantz.fi/index.php?page=software g3data homepage]<br />
*[[GIFMerge]] -- [http://www.the-labs.com/GIFMerge/ GIFMerge homepage]<br />
*[[Gifsicle]]<br />
<br />
== Commercial codes ==<br />
<br />
=== Solvers ===<br />
<br />
*[[ADINA-F]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[ADINA-FSI]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[ANSWER]] -- [http://www.acricfd.com/ ACRi's homepage]<br />
*[http://www.cfd-online.com/W/index.php?title=CFD%2B%2B CFD++] -- [http://www.metacomptech.com Metacomp Techonlogies' homepage]<br />
*[[CFD2000]] -- [http://www.adaptive-research.com/ Adaptive Research's homepage]<br />
*[[CFD-FASTRAN]] -- [http://www.esi-group.com/SimulationSoftware/advanced.html ESI Group's homepage]<br />
*[[CFD-ACE]] -- [http://www.esi-group.com/SimulationSoftware/advanced.html ESI Group's homepage]<br />
*[[CFX]] -- [http://www.ansys.com/ Ansys' homepage]<br />
*[[EFD]] -- [http://www.nika.biz/ NIKA's homepage]<br />
*[[FENSAP-ICE]] -- [http://www.newmerical.com/ NTI' homepage]<br />
*[[FINE]] -- [http://www.numeca.be/ Numeca's homepage]<br />
*[[FIRE]] -- [http://www.avl.com/ AVL's homepage]<br />
*[[FLACS]] -- [http://www.gexcon.com/index.php?src=flacs/overview.html GexCon's homepage]<br />
*[[FLOW-3D]] -- [http://www.flow3d.com/ Flow Science's homepage]<br />
*[[FLOWVISION]] -- [http://www.fv-tech.com FlowVision's homepage]<br />
*[[FLUENT]] -- [http://www.fluent.com Fluent's homepage]<br />
*[[FluSol]] -- [http://www.cfd-rocket.com FluSol's hompage]*[[J-FLO]] -- [http://www.newmerical.com NTI's homepage]<br />
*[[Flowz]]--[http://www.zeusnumerix.com Zeus Numerix's homepage ]<br />
*[[KINetics Reactive Flows]] -- [http://www.ReactionDesign.com Reaction Design's homepage]<br />
*[[KIVA]]--[http://www.lanl.gov/orgs/t/t3/codes/kiva.shtml Los Alamos homepage]<br />
*[[NOGRID FPM]] -- [http://www.no-grid.com NOGRIDS's homepage]<br />
*[[PHOENICS]] -- [http://www.cham.co.uk CHAM's homepage]<br />
*[[STAR-CD]] -- [http://www.cd-adapco.com CD-adapco's homepage]<br />
*[[STAR-CCMplus]] -- [http://www.cd-adapco.com CD-adapco's homepage]<br />
*[[Turb'Flow]] -- [http://www.fluorem.com Fluorem's hompage]<br />
<br />
=== Grid generation ===<br />
<br />
*[[ADINA-AUI]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[CFD-GEOM]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFD-VISCART]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFDExpert-GridZ ]] --[http://www.zeusnumerix.com/ Zeus Numerix's homepage]<br />
*[[Gridgen]] -- [http://www.pointwise.com/ Pointwise's homepage]<br />
*[[GridPro]] -- [http://www.gridpro.com/ PDC's homepage]<br />
*[[Harpoon]] -- [http://www.ensight.com/ CEI's homepage]<br />
*[[ICEM CFD ]] -- [http://www.ansys.com/ ANSYS' homepage]<br />
<br />
=== Visualization ===<br />
<br />
*[[ADINA-AUI]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[CFD-VIEW]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFX-Post]] -- [http://www.ansys.com/ ANSYS' homepage]<br />
*[[EnSight]] -- [http://www.ensight.com/ CEI's homepage]<br />
*[[Fieldview]] -- [http://www.ilight.com/ Intelligent Light's homepage]<br />
*[[Tecplot]] -- [http://www.tecplot.com/ Tecplot's homepage]<br />
*[[ViewZ]] -- [http://www.zeusnumerix.com/ Zeus Numerix's homepage]<br />
<br />
=== Systems ===<br />
<br />
*[[ADINA]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[Flownex]] -- [http://www.flownex.com/ Flownex's homepage]<br />
<br />
== Online tools and services ==<br />
<br />
*[[CFDNet]] -- [http://www.cfdnet.com/ CFDNet homepage]</div>Zxaarhttp://www.cfd-online.com/Wiki/CodesCodes2007-02-24T01:08:35Z<p>Zxaar: /* Solvers */</p>
<hr />
<div>An overview of both free and commercial CFD software.<br />
<br />
== Free codes ==<br />
<br />
This section lists codes that are in the public domain, and codes that are available under GPL, BSD or similar licenses.<br />
<br />
=== Solvers ===<br />
<br />
*[[ADFC]] -- [http://adfc.sourceforge.net/index.html ADFC homepage]<br />
*[[Diagonalized Upwind Navier Stokes]] -- [http://duns.sourceforge.net DUNS homepage]<br />
*[[Dolfyn]] -- [http://www.dolfyn.net/dolfyn/index_en.html dolfyn homepage]<br />
*[[Edge]] -- [http://www.edge.foi.se/ Edge homepage]<br />
*[[ELMER]] -- [http://www.csc.fi/elmer/ ELMER homepage]<br />
*[[FreeFEM]] -- [http://www.freefem.org FreeFEM homepage]<br />
*[[Gerris Flow Solver]] -- [http://gfs.sourceforge.net/ Gerris Flow Solver homepage]<br />
*[[IMTEK Mathematica Supplement (IMS)]] -- [http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/ IMTEK Mathematica Supplement (IMS) homepage]<br />
*[[iNavier]] -- [http://inavier.sourceforge.net/ iNavier Solver (Sourceforge.net page)]<br />
*[[MFIX]] -- [http://www.mfix.org Computational multiphase flow homepage]<br />
*[[NaSt2D-2.0]] -- [http://home.arcor.de/drklaus.bauerfeind/nast/eNaSt2D.html NaSt2D-2.0 homepage]<br />
*[[NSC2KE]] -- [http://www-rocq1.inria.fr/gamma/cdrom/www/nsc2ke/eng.htm NSC2KE homepage]<br />
*[[OpenFlower]] -- [http://sourceforge.net/projects/openflower/ OpenFlower homepage]<br />
*[[OpenFOAM]] -- [http://www.openfoam.org/ OpenFOAM homepage]<br />
*[[OpenFVM]] -- [http://openfvm.sourceforge.net/ OpenFVM homepage]<br />
*[[PETSc-FEM]] -- [http://www.cimec.org.ar/petscfem PETSc-FEM homepage]<br />
*[[PP3D]] -- [http://www.featflow.de/ parpp3d++ homepage]<br />
*[[SLFCFD]] -- [http://slfcfd.sourceforge.net SLFCFD homepage]<br />
*[[Tochnog]] -- [http://tochnog.sourceforge.net Tochnog homepage]<br />
*[[Typhon solver]] -- [http://typhon.sf.net Typhon solver homepage]<br />
<br />
=== Grid generation ===<br />
<br />
*[[Delaundo]] -- [http://www.cerfacs.fr/~muller/delaundo.html Dalaundo homepage]<br />
*[[GMSH]] -- [http://www.geuz.org/gmsh/ GMSH hompage]<br />
*[[NETGEN]] -- [http://www.hpfem.jku.at/netgen/ NETGEN homepage]<br />
*[[SALOME]] -- [http://www.salome-platform.org SALOME homepage]<br />
*[[TETGEN]] -- [http://tetgen.berlios.de/ TETGEN hompage]<br />
*[[Triangle]] -- [http://www.cs.cmu.edu/~quake/triangle.html Trangle homepage]<br />
<br />
=== Visualization ===<br />
<br />
*[[GMV]] -- [http://www-xdiv.lanl.gov/XCM/gmv/ GMV homepage]<br />
*[[Gnuplot]] -- [http://www.gnuplot.info/ gnuplot homepage]<br />
*[[Mayavi]] -- [http://mayavi.sourceforge.net/ MayaVi homepage]<br />
*[[OpenDX]] <br />
*[[ParaView]] -- [http://www.paraview.org/HTML/Index.html ParaView homepage]<br />
*[[Vigie]] -- [http://www-sop.inria.fr/sinus/Softs/vigie.html Vigie homepage]<br />
*[[Visit]]<br />
*[[vtk]] -- [http://www.vtk.org vtk homepage]<br />
*[[vtk.Net]] -- [http://vtkdotnet.sourceforge.net/ vtk.Net homepage]<br />
<br />
=== Miscellaneous ===<br />
<br />
*[[Engauge Digitizer]]<br />
*[[Ftnchek]]<br />
*[[g3data]] -- [http://www.frantz.fi/index.php?page=software g3data homepage]<br />
*[[GIFMerge]] -- [http://www.the-labs.com/GIFMerge/ GIFMerge homepage]<br />
*[[Gifsicle]]<br />
<br />
== Commercial codes ==<br />
<br />
=== Solvers ===<br />
<br />
*[[ADINA-F]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[ADINA-FSI]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[ANSWER]] -- [http://www.acricfd.com/ ACRi's homepage]<br />
*[http://www.cfd-online.com/W/index.php?title=CFD%2B%2B CFD++] -- [http://www.metacomptech.com Metacomp Techonlogies' homepage]<br />
*[[CFD2000]] -- [http://www.adaptive-research.com/ Adaptive Research's homepage]<br />
*[[CFD-FASTRAN]] -- [http://www.esi-group.com/SimulationSoftware/advanced.html ESI Group's homepage]<br />
*[[CFD-ACE]] -- [http://www.esi-group.com/SimulationSoftware/advanced.html ESI Group's homepage]<br />
*[[CFX]] -- [http://www.ansys.com/ Ansys' homepage]<br />
*[[EFD]] -- [http://www.nika.biz/ NIKA's homepage]<br />
*[[FENSAP-ICE]] -- [http://www.newmerical.com/ NTI' homepage]<br />
*[[FINE]] -- [http://www.numeca.be/ Numeca's homepage]<br />
*[[FIRE]] -- [http://www.avl.com/ AVL's homepage]<br />
*[[FLACS]] -- [http://www.gexcon.com/index.php?src=flacs/overview.html GexCon's homepage]<br />
*[[FLOW-3D]] -- [http://www.flow3d.com/ Flow Science's homepage]<br />
*[[FLOWVISION]] -- [http://www.fv-tech.com FlowVision's homepage]<br />
*[[FLUENT]] -- [http://www.fluent.com Fluent's homepage]<br />
*[[FluSol]] -- [http://www.cfd-rocket.com FluSol's hompage]*[[J-FLO]] -- [http://www.newmerical.com NTI's homepage]<br />
*[[Flowz]]--[http://www.zeusnumerix.com Zeus Numerix's homepage ]<br />
*[[KINetics Reactive Flows]] -- [http://www.ReactionDesign.com Reaction Design's homepage]<br />
*[[KIVA]]--[http://www.lanl.gov/orgs/t/t3/codes/kiva.shtml Los Alamos homepage]<br />
*[[NOGRID FPM]] -- [http://www.no-grid.com NOGRIDS's homepage]<br />
*[[PHOENICS]] -- [http://www.cham.co.uk CHAM's homepage]<br />
*[[STAR-CD]] -- [http://www.cd-adapco.com CD-adapco's homepage]<br />
*[[STAR-CCMplus]] -- [http://www.cd-adapco.com CD-adapco's homepage]<br />
*[[Turb'Flow]] -- [http://www.fluorem.com Fluorem's hompage]<br />
<br />
=== Grid generation ===<br />
<br />
*[[ADINA-AUI]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[CFD-GEOM]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFD-VISCART]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFDExpert-GridZ ]] --[http://www.zeusnumerix.com/ Zeus Numerix's homepage]<br />
*[[Gridgen]] -- [http://www.pointwise.com/ Pointwise's homepage]<br />
*[[GridPro]] -- [http://www.gridpro.com/ PDC's homepage]<br />
*[[Harpoon]] -- [http://www.ensight.com/ CEI's homepage]<br />
*[[ICEM CFD ]] -- [http://www.ansys.com/ ANSYS' homepage]<br />
<br />
=== Visualization ===<br />
<br />
*[[ADINA-AUI]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[CFD-VIEW]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFX-Post]] -- [http://www.ansys.com/ ANSYS' homepage]<br />
*[[EnSight]] -- [http://www.ensight.com/ CEI's homepage]<br />
*[[Fieldview]] -- [http://www.ilight.com/ Intelligent Light's homepage]<br />
*[[Tecplot]] -- [http://www.tecplot.com/ Tecplot's homepage]<br />
*[[ViewZ]] -- [http://www.zeusnumerix.com/ Zeus Numerix's homepage]<br />
<br />
=== Systems ===<br />
<br />
*[[ADINA]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[Flownex]] -- [http://www.flownex.com/ Flownex's homepage]<br />
<br />
== Online tools and services ==<br />
<br />
*[[CFDNet]] -- [http://www.cfdnet.com/ CFDNet homepage]</div>Zxaarhttp://www.cfd-online.com/Wiki/CodesCodes2007-02-23T10:59:21Z<p>Zxaar: /* Solvers */</p>
<hr />
<div>An overview of both free and commercial CFD software.<br />
<br />
== Free codes ==<br />
<br />
This section lists codes that are in the public domain, and codes that are available under GPL, BSD or similar licenses.<br />
<br />
=== Solvers ===<br />
<br />
*[[ADFC]] -- [http://adfc.sourceforge.net/index.html ADFC homepage]<br />
*[[Diagonalized Upwind Navier Stokes]] -- [http://duns.sourceforge.net DUNS homepage]<br />
*[[Dolfyn]] -- [http://www.dolfyn.net/dolfyn/index_en.html dolfyn homepage]<br />
*[[Edge]] -- [http://www.edge.foi.se/ Edge homepage]<br />
*[[ELMER]] -- [http://www.csc.fi/elmer/ ELMER homepage]<br />
*[[FreeFEM]] -- [http://www.freefem.org FreeFEM homepage]<br />
*[[Gerris Flow Solver]] -- [http://gfs.sourceforge.net/ Gerris Flow Solver homepage]<br />
*[[IMTEK Mathematica Supplement (IMS)]] -- [http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/ IMTEK Mathematica Supplement (IMS) homepage]<br />
*[[MFIX]] -- [http://www.mfix.org Computational multiphase flow homepage]<br />
*[[NaSt2D-2.0]] -- [http://home.arcor.de/drklaus.bauerfeind/nast/eNaSt2D.html NaSt2D-2.0 homepage]<br />
*[[NSC2KE]] -- [http://www-rocq1.inria.fr/gamma/cdrom/www/nsc2ke/eng.htm NSC2KE homepage]<br />
*[[OpenFlower]] -- [http://sourceforge.net/projects/openflower/ OpenFlower homepage]<br />
*[[OpenFOAM]] -- [http://www.openfoam.org/ OpenFOAM homepage]<br />
*[[OpenFVM]] -- [http://openfvm.sourceforge.net/ OpenFVM homepage]<br />
*[[PETSc-FEM]] -- [http://www.cimec.org.ar/petscfem PETSc-FEM homepage]<br />
*[[PP3D]] -- [http://www.featflow.de/ parpp3d++ homepage]<br />
*[[SLFCFD]] -- [http://slfcfd.sourceforge.net SLFCFD homepage]<br />
*[[Tochnog]] -- [http://tochnog.sourceforge.net Tochnog homepage]<br />
*[[Typhon solver]] -- [http://typhon.sf.net Typhon solver homepage]<br />
*[[iNavier]] -- [http://sourceforge.net/projects/inavier/ iNavier Solver (Sourceforge.net page)]<br />
<br />
=== Grid generation ===<br />
<br />
*[[BAMG]]<br />
*[[Delaundo]]<br />
*[[Triangle]]<br />
*[[GMSH]] -- [http://www.geuz.org/gmsh/ GMSH hompage]<br />
*[[TETGEN]] -- [http://tetgen.berlios.de/ TETGEN hompage]<br />
*[[NETGEN]] -- [http://www.hpfem.jku.at/netgen/ NETGEN homepage]<br />
*[[SALOME]] -- [http://www.salome-platform.org SALOME homepage]<br />
<br />
=== Visualization ===<br />
<br />
*[[GMV]] -- [http://www-xdiv.lanl.gov/XCM/gmv/ GMV homepage]<br />
*[[Gnuplot]] -- [http://www.gnuplot.info/ gnuplot homepage]<br />
*[[Mayavi]] -- [http://mayavi.sourceforge.net/ MayaVi homepage]<br />
*[[OpenDX]] <br />
*[[ParaView]] -- [http://www.paraview.org/HTML/Index.html ParaView homepage]<br />
*[[Vigie]] -- [http://www-sop.inria.fr/sinus/Softs/vigie.html Vigie homepage]<br />
*[[Visit]]<br />
*[[vtk]] -- [http://www.vtk.org vtk homepage]<br />
*[[vtk.Net]] -- [http://vtkdotnet.sourceforge.net/ vtk.Net homepage]<br />
<br />
=== Miscellaneous ===<br />
<br />
*[[Engauge Digitizer]]<br />
*[[Ftnchek]]<br />
*[[g3data]] -- [http://www.frantz.fi/index.php?page=software g3data homepage]<br />
*[[GIFMerge]] -- [http://www.the-labs.com/GIFMerge/ GIFMerge homepage]<br />
*[[Gifsicle]]<br />
<br />
== Commercial codes ==<br />
<br />
=== Solvers ===<br />
<br />
*[[ADINA-F]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[ADINA-FSI]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[ANSWER]] -- [http://www.acricfd.com/ ACRi's homepage]<br />
*[http://www.cfd-online.com/W/index.php?title=CFD%2B%2B CFD++] -- [http://www.metacomptech.com Metacomp Techonlogies' homepage]<br />
*[[CFD2000]] -- [http://www.adaptive-research.com/ Adaptive Research's homepage]<br />
*[[CFD-FASTRAN]] -- [http://www.esi-group.com/SimulationSoftware/advanced.html ESI Group's homepage]<br />
*[[CFD-ACE]] -- [http://www.esi-group.com/SimulationSoftware/advanced.html ESI Group's homepage]<br />
*[[CFX]] -- [http://www.ansys.com/ Ansys' homepage]<br />
*[[EFD]] -- [http://www.nika.biz/ NIKA's homepage]<br />
*[[FENSAP-ICE]] -- [http://www.newmerical.com/ NTI' homepage]<br />
*[[FINE]] -- [http://www.numeca.be/ Numeca's homepage]<br />
*[[FIRE]] -- [http://www.avl.com/ AVL's homepage]<br />
*[[FLACS]] -- [http://www.gexcon.com/index.php?src=flacs/overview.html GexCon's homepage]<br />
*[[FLOW-3D]] -- [http://www.flow3d.com/ Flow Science's homepage]<br />
*[[FLOWVISION]] -- [http://www.fv-tech.com FlowVision's homepage]<br />
*[[FLUENT]] -- [http://www.fluent.com Fluent's homepage]<br />
*[[J-FLO]] -- [http://www.newmerical.com NTI's homepage]<br />
*[[KINetics Reactive Flows]] -- [http://www.ReactionDesign.com Reaction Design's homepage]<br />
*[[NOGRID FPM]] -- [http://www.no-grid.com NOGRIDS's homepage]<br />
*[[PHOENICS]] -- [http://www.cham.co.uk CHAM's homepage]<br />
*[[STAR-CD]] -- [http://www.cd-adapco.com CD-adapco's homepage]<br />
*[[STAR-CCMplus]] -- [http://www.cd-adapco.com CD-adapco's homepage]<br />
*[[Turb'Flow]] -- [http://www.fluorem.com Fluorem's hompage]<br />
*[[FluSol]] -- [http://www.cfd-rocket.com FluSol's hompage]<br />
*[[KIVA]]--[http://www.lanl.gov/orgs/t/t3/codes/kiva.shtml Los Alamos homepage]<br />
*[[Flowz]]--[http://www.zeusnumerix.com Zeus Numerix's homepage ]<br />
<br />
=== Grid generation ===<br />
<br />
*[[ADINA-AUI]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[Gridgen]] -- [http://www.pointwise.com/ Pointwise's homepage]<br />
*[[GridPro]] -- [http://www.gridpro.com/ PDC's homepage]<br />
*[[Harpoon]] -- [http://www.ensight.com/ CEI's homepage]<br />
*[[CFD-GEOM]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFD-VISCART]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFDExpert-GridZ ]] --[http://www.zeusnumerix.com/ Zeus Numerix's homepage]<br />
*[[ICEM CFD ]] -- [http://www.ansys.com/ ANSYS' homepage]<br />
<br />
=== Visualization ===<br />
<br />
*[[ADINA-AUI]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[EnSight]] -- [http://www.ensight.com/ CEI's homepage]<br />
*[[Fieldview]] -- [http://www.ilight.com/ Intelligent Light's homepage]<br />
*[[Tecplot]] -- [http://www.tecplot.com/ Tecplot's homepage]<br />
*[[CFD-VIEW]] -- [http://www.esi-group.com/ ESI's homepage]<br />
*[[CFX-Post]] -- [http://www.ansys.com/ ANSYS' homepage]<br />
*[[ViewZ]] -- [http://www.zeusnumerix.com/ Zeus Numerix's homepage]<br />
<br />
=== Systems ===<br />
<br />
*[[ADINA]] -- [http://www.adina.com/index.html ADINA's homepage]<br />
*[[Flownex]] -- [http://www.flownex.com/ Flownex's homepage]<br />
<br />
== Online tools and services ==<br />
<br />
*[[CFDNet]] -- [http://www.cfdnet.com/ CFDNet homepage]</div>Zxaarhttp://www.cfd-online.com/Wiki/User:ZxaarUser:Zxaar2005-12-16T14:00:51Z<p>Zxaar: </p>
<hr />
<div>I am working with Dunlop Japan, in aerodynamics field.<br><br />
I am graduate from IIT-Delhi in chemical engineering field. <br><br />
web: www.zxaar.com</div>Zxaarhttp://www.cfd-online.com/Wiki/User:ZxaarUser:Zxaar2005-12-16T14:00:21Z<p>Zxaar: </p>
<hr />
<div>I am working with Dunlop Japan, in aerodynamics field.<br />
I am graduate from IIT-Delhi in chemical engineer.<br />
web: www.zxaar.com</div>Zxaarhttp://www.cfd-online.com/Wiki/Fluent_FAQFluent FAQ2005-11-30T01:36:25Z<p>Zxaar: </p>
<hr />
<div>This section is empty. This is just a suggestion on how to structure it. Please feel free to add questions and answers here!<br />
<br />
<br />
== FLUENT ==<br />
=== Solver Related ===<br />
==== What does the floating point error mean? How can I avoid it? ====<br />
<br />
The floating point error has been reported many times and discussed a lot. Here are some of the answers found in the Fluent Forum:<br />
<br />
'''SOLVER AND ITERATION''' -----I think if you set shorter time step, it may be good. Or changing little Under-Relaxiation-Factors, it may be good. In my experience, I set 1/3 Under-Relaxiation-Factors as default.� -----�also lower the values of under relaxation factor and use the coupled implicit solver� -----�Try to change under-relaxation factors and if it is unsteady problem maybe time step is to large.� -----�you can improve the ratio in the solve--control--limits, maybe that can help.� -----�you will need to decrease the Courant number� -----�If you still get the error, initialize the domain with nothing to 'Compute from...' Then click 'init'. Again select the surface from which you want to compute the initial values & iterate. This should work.� -----�Another reason could be a to high courant number - that means, that the steps between two iterations are too large and the change in the results is too large as well (high residuals)�<br />
<br />
'''GRID PROBLEMS''' -----�this error comes when I start scaling grid. in gambit, all my dimension is in mm, when in fluent i convert it in meter using buttone SCALE. after it, when i iterate, about hundred iteration, this error appeared. but when i not scale my drawing to m...and let it be as in gambit..then the iteration is success. -----�hi I think you should check your mesh grid mesh is very high. your problem solve by selection a low mesh.� -----�Your mesh is so heavy that your computers resources are not enough. try to use coarser mesh.�<br />
<br />
'''BOUNDARY CONDITIONS''' -----�In my case I had set a wall boundary condition instead of an axis boundary condition and then FLuent refuses to calculate telling me 'floating point error'.� -----�Your Boudary Conditions do not represent real physis.� -----�wrong boundary condition definition might cause the floating point error. For example setting an internal boundary as interior� -----�Once I had the problem, simulating a 2D chamber with a symmetry BC. I set the symmetry somewhere as �axe symmetric� and the floating point error occur� -----�check the turbulence parameter you set. reduce the turbulence intensity to less that one for first, say 50 iterations.<br />
<br />
'''USING A UDF''' -----�What I mean is really often when people creates UDF they generally forget that for the first iteration some variable can be zero. Therefore if you are divided a number by zero your solver will blow up telling you 'non floating error'. 'non' means 'not a number'. Depending on your UDF this kind of error does not effectively happens at the first iteration. An example, if you are simulated a domain with a stagnant water as initial condition and you are calculated for the first iteration something like 1/Re therefore lets call it BOOM !!! because Re=0 . To find this kind of think there a simple way : reread your UDF.�<br />
<br />
'''MULTI PROCESSOR ISSUES''' -----"I've had similar problems recently with floating point errors on a multi processor simulation. The solution for my problem seems to be to run on a single processor, where it runs fine....?�<br />
<br />
'''WRONG INITIATION''' ----- Initiating the case with wrong conditions may lead to floating point error when the iterations start.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
=== Models Related ===<br />
==== What is the turbulent viscosity ratio warning and how can I handle? ====<br />
<br />
==== How can I determine the inputs for a porous media or porous jump from flow versus pressure drop data? ====<br />
<br />
==== How do I model heat conduction in a composite wall? ====<br />
<br />
==== What pressures should be specified at inlets and outlets for buoyancy flow problems? ====<br />
<br />
==== Are there any general guidelines on selecting a turbulence model? ====<br />
<br />
==== How can both turbulent and laminar flow be included in one model? ====<br />
<br />
==== How to start a 3D simulation with an compressible medium and temperature changes? What is important to consider ====<br />
<br />
<br />
<br />
=== Solution Methodology === <br />
==== How do i carry out rotating body analysis, eg a rotating sphere or cylinder in flow? ====<br />
==== How do i get better and faster convergence? ====<br />
==== What is the role of under-relaxation parameters? What should be the optimum choice of these parameters? ====<br />
They limit the influence of the previous iteration over the present one. If you choose small values it may prevent oscillations in residuum developing. At the same time the solution may need more time to converge. <br />
Keep the default values as they are given in FLUENT. You can decrease them gradually if necessary. Momentum 0.6, pressure 0.1, k 0.4, eps 0.4, mass source 1, viscosity 1.<br />
<br />
<br />
=== Tips === <br />
==== How to merge two mesh files and make one? ====<br />
To merge two mesh files the suggested utility is tmerge. The syntax of tmerge is simple.<br><br />
<i>utility tmerge -3d file1 file2 finalfile </i> <br><br />
To join the two interior faces use: <br><br />
<i>Grid->Fuse</i> <br><br />
from the menu with Fluent.<br />
<br />
==== How to run multiple cases in batch mode ==== <br />
This could be achieved by running it from journal file. The example journal file that runs two cases is given as <br><br />
<i><br />
file read-case-data xxx1.cas <br><br />
solve dual-time-iterate yyy1 <br><br />
file write-case-data zzz1.cas <br><br />
file read-case-data xxx2.cas <br><br />
yes <b>(comment: for discard cas dialog) </b><br><br />
solve dual-time-iterate yyy2 <br><br />
file write-case-data zzz2.cas <br></i><br />
<br />
<br><br />
<br><br />
have a look at this discussion: <br><br />
http://www.cfd-online.com/Forum/fluent_archive.cgi?read=32615<br />
<br />
==== Want to export Fieldview data for postprocssing during iterations ====<br />
This could be done with the help of menu <b>solve->Execute Commands </b>. <br />
Here are two examples: <br><br />
Steady Case <br><br />
<b><br />
:file/export/fug/File_grid-%n <br><br />
:file/export/fud/File_data-%n pressure velocity-magnitude x-velocity y-velocity z-velocity () <br> </b><br />
Unsteady Case <br><br />
<b><br />
:file/export/fug/File_grid-%t <br><br />
:file/export/fud/File_data-%t pressure velocity-magnitude x-velocity y-velocity z-velocity () <br> </b><br />
<br />
You can chose the frequency of export from the <b>Execute Command</b> panel. <br />
<br />
==== What does the abbreviation mean?====<br />
<br />
CFD = Computational Fluid dynamics <br><br />
FEM = Finite element model <br><br />
FVM = Finite Volume Method<br><br />
FDM = <br><br />
UDF = User defined function <br><br />
PDF = Probability Density Function<br><br />
URF = Under Relaxation Factor<br><br />
<br />
== FloWizard==<br />
<br />
== FIDAP==<br />
<br />
== POLYFLOW ==<br />
<br />
== Pre-processors ==<br />
<br />
=== Gambit ===<br />
<br />
=== Gambit Turbo ===<br />
<br />
=== TGrid ===<br />
<br />
== Application specific codes ==<br />
<br />
=== Icepak ===<br />
<br />
=== Airpak ===<br />
<br />
=== MixSim ===<br />
<br />
== Educational codes ==<br />
<br />
=== FlowLab ===<br />
<br />
<br />
[[Category: FAQ's]]<br />
<br />
{{stub}}</div>Zxaarhttp://www.cfd-online.com/Wiki/Fluent_FAQFluent FAQ2005-11-24T02:40:32Z<p>Zxaar: </p>
<hr />
<div>This section is empty. This is just a suggestion on how to structure it. Please feel free to add questions and answers here!<br />
<br />
<br />
== FLUENT ==<br />
=== Solver Related ===<br />
==== What does the floating point error mean? How can I avoid it? ====<br />
<br />
The floating point error has been reported many times and discussed a lot. Here are some of the answers found in the Fluent Forum:<br />
<br />
'''SOLVER AND ITERATION''' -----I think if you set shorter time step, it may be good. Or changing little Under-Relaxiation-Factors, it may be good. In my experience, I set 1/3 Under-Relaxiation-Factors as default.� -----�also lower the values of under relaxation factor and use the coupled implicit solver� -----�Try to change under-relaxation factors and if it is unsteady problem maybe time step is to large.� -----�you can improve the ratio in the solve--control--limits, maybe that can help.� -----�you will need to decrease the Courant number� -----�If you still get the error, initialize the domain with nothing to 'Compute from...' Then click 'init'. Again select the surface from which you want to compute the initial values & iterate. This should work.� -----�Another reason could be a to high courant number - that means, that the steps between two iterations are too large and the change in the results is too large as well (high residuals)�<br />
<br />
'''GRID PROBLEMS''' -----�this error comes when I start scaling grid. in gambit, all my dimension is in mm, when in fluent i convert it in meter using buttone SCALE. after it, when i iterate, about hundred iteration, this error appeared. but when i not scale my drawing to m...and let it be as in gambit..then the iteration is success. -----�hi I think you should check your mesh grid mesh is very high. your problem solve by selection a low mesh.� -----�Your mesh is so heavy that your computers resources are not enough. try to use coarser mesh.�<br />
<br />
'''BOUNDARY CONDITIONS''' -----�In my case I had set a wall boundary condition instead of an axis boundary condition and then FLuent refuses to calculate telling me 'floating point error'.� -----�Your Boudary Conditions do not represent real physis.� -----�wrong boundary condition definition might cause the floating point error. For example setting an internal boundary as interior� -----�Once I had the problem, simulating a 2D chamber with a symmetry BC. I set the symmetry somewhere as �axe symmetric� and the floating point error occur� -----�check the turbulence parameter you set. reduce the turbulence intensity to less that one for first, say 50 iterations.<br />
<br />
'''USING A UDF''' -----�What I mean is really often when people creates UDF they generally forget that for the first iteration some variable can be zero. Therefore if you are divided a number by zero your solver will blow up telling you 'non floating error'. 'non' means 'not a number'. Depending on your UDF this kind of error does not effectively happens at the first iteration. An example, if you are simulated a domain with a stagnant water as initial condition and you are calculated for the first iteration something like 1/Re therefore lets call it BOOM !!! because Re=0 . To find this kind of think there a simple way : reread your UDF.�<br />
<br />
'''MULTI PROCESSOR ISSUES''' -----"I've had similar problems recently with floating point errors on a multi processor simulation. The solution for my problem seems to be to run on a single processor, where it runs fine....?�<br />
<br />
'''WRONG INITIATION''' ----- Initiating the case with wrong conditions may lead to floating point error when the iterations start.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
=== Models Related ===<br />
==== What is the turbulent viscosity ratio warning and how can I handle? ====<br />
<br />
==== How can I determine the inputs for a porous media or porous jump from flow versus pressure drop data? ====<br />
<br />
==== How do I model heat conduction in a composite wall? ====<br />
<br />
==== What pressures should be specified at inlets and outlets for buoyancy flow problems? ====<br />
<br />
==== Are there any general guidelines on selecting a turbulence model? ====<br />
<br />
==== How can both turbulent and laminar flow be included in one model? ====<br />
<br />
==== How to start a 3D simulation with an compressible medium and temperature changes? What is important to consider ====<br />
<br />
<br />
<br />
=== Solution Methodology === <br />
==== How do i carry out rotating body analysis, eg a rotating sphere or cylinder in flow? ====<br />
==== How do i get better and faster convergence? ====<br />
==== What is the role of under-relaxation parameters? What should be the optimum choice of these parameters? ====<br />
They limit the influence of the previous iteration over the present one. If you choose small values it may prevent oscillations in residuum developing. At the same time the solution may need more time to converge. <br />
Keep the default values as they are given in FLUENT. You can decrease them gradually if necessary. Momentum 0.6, pressure 0.1, k 0.4, eps 0.4, mass source 1, viscosity 1.<br />
<br />
<br />
=== Tips === <br />
==== How to merge two mesh files and make one? ====<br />
To merge two mesh files the suggested utility is tmerge. The syntax of tmerge is simple.<br><br />
<i>utility tmerge -3d file1 file2 finalfile </i> <br><br />
To join the two interior faces use: <br><br />
<i>Grid->Fuse</i> <br><br />
from the menu with Fluent.<br />
<br />
==== How to run multiple cases in batch mode ==== <br />
This could be achieved by running it from journal file. The example journal file that runs two cases is given as <br><br />
<i><br />
file read-case-data xxx1.cas <br><br />
solve dual-time-iterate yyy1 <br><br />
file write-case-data zzz1.cas <br><br />
file read-case-data xxx2.cas <br><br />
yes <b>(comment: for discard cas dialog) </b><br><br />
solve dual-time-iterate yyy2 <br><br />
file write-case-data zzz2.cas <br></i><br />
<br />
<br />
<br />
<br />
==== What does the abbreviation mean?====<br />
<br />
CFD = Computational Fluid dynamics<br />
FEM = Finite element model<br />
UDF = User defined function<br />
<br />
== FloWizard==<br />
<br />
== FIDAP==<br />
<br />
== POLYFLOW ==<br />
<br />
== Pre-processors ==<br />
<br />
=== Gambit ===<br />
<br />
=== Gambit Turbo ===<br />
<br />
=== TGrid ===<br />
<br />
== Application specific codes ==<br />
<br />
=== Icepak ===<br />
<br />
=== Airpak ===<br />
<br />
=== MixSim ===<br />
<br />
== Educational codes ==<br />
<br />
=== FlowLab ===<br />
<br />
<br />
[[Category: FAQ's]]<br />
<br />
{{stub}}</div>Zxaarhttp://www.cfd-online.com/Wiki/Fluent_FAQFluent FAQ2005-11-24T02:39:05Z<p>Zxaar: </p>
<hr />
<div>This section is empty. This is just a suggestion on how to structure it. Please feel free to add questions and answers here!<br />
<br />
<br />
== FLUENT ==<br />
== Solver Related ==<br />
==== What does the floating point error mean? How can I avoid it? ====<br />
<br />
The floating point error has been reported many times and discussed a lot. Here are some of the answers found in the Fluent Forum:<br />
<br />
'''SOLVER AND ITERATION''' -----I think if you set shorter time step, it may be good. Or changing little Under-Relaxiation-Factors, it may be good. In my experience, I set 1/3 Under-Relaxiation-Factors as default.� -----�also lower the values of under relaxation factor and use the coupled implicit solver� -----�Try to change under-relaxation factors and if it is unsteady problem maybe time step is to large.� -----�you can improve the ratio in the solve--control--limits, maybe that can help.� -----�you will need to decrease the Courant number� -----�If you still get the error, initialize the domain with nothing to 'Compute from...' Then click 'init'. Again select the surface from which you want to compute the initial values & iterate. This should work.� -----�Another reason could be a to high courant number - that means, that the steps between two iterations are too large and the change in the results is too large as well (high residuals)�<br />
<br />
'''GRID PROBLEMS''' -----�this error comes when I start scaling grid. in gambit, all my dimension is in mm, when in fluent i convert it in meter using buttone SCALE. after it, when i iterate, about hundred iteration, this error appeared. but when i not scale my drawing to m...and let it be as in gambit..then the iteration is success. -----�hi I think you should check your mesh grid mesh is very high. your problem solve by selection a low mesh.� -----�Your mesh is so heavy that your computers resources are not enough. try to use coarser mesh.�<br />
<br />
'''BOUNDARY CONDITIONS''' -----�In my case I had set a wall boundary condition instead of an axis boundary condition and then FLuent refuses to calculate telling me 'floating point error'.� -----�Your Boudary Conditions do not represent real physis.� -----�wrong boundary condition definition might cause the floating point error. For example setting an internal boundary as interior� -----�Once I had the problem, simulating a 2D chamber with a symmetry BC. I set the symmetry somewhere as �axe symmetric� and the floating point error occur� -----�check the turbulence parameter you set. reduce the turbulence intensity to less that one for first, say 50 iterations.<br />
<br />
'''USING A UDF''' -----�What I mean is really often when people creates UDF they generally forget that for the first iteration some variable can be zero. Therefore if you are divided a number by zero your solver will blow up telling you 'non floating error'. 'non' means 'not a number'. Depending on your UDF this kind of error does not effectively happens at the first iteration. An example, if you are simulated a domain with a stagnant water as initial condition and you are calculated for the first iteration something like 1/Re therefore lets call it BOOM !!! because Re=0 . To find this kind of think there a simple way : reread your UDF.�<br />
<br />
'''MULTI PROCESSOR ISSUES''' -----"I've had similar problems recently with floating point errors on a multi processor simulation. The solution for my problem seems to be to run on a single processor, where it runs fine....?�<br />
<br />
'''WRONG INITIATION''' ----- Initiating the case with wrong conditions may lead to floating point error when the iterations start.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Models Related ==<br />
==== What is the turbulent viscosity ratio warning and how can I handle? ====<br />
<br />
==== How can I determine the inputs for a porous media or porous jump from flow versus pressure drop data? ====<br />
<br />
==== How do I model heat conduction in a composite wall? ====<br />
<br />
==== What pressures should be specified at inlets and outlets for buoyancy flow problems? ====<br />
<br />
==== Are there any general guidelines on selecting a turbulence model? ====<br />
<br />
==== How can both turbulent and laminar flow be included in one model? ====<br />
<br />
==== How to start a 3D simulation with an compressible medium and temperature changes? What is important to consider ====<br />
<br />
<br />
<br />
== Solution Methodology == <br />
==== How do i carry out rotating body analysis, eg a rotating sphere or cylinder in flow? ====<br />
==== How do i get better and faster convergence? ====<br />
==== What is the role of under-relaxation parameters? What should be the optimum choice of these parameters? ====<br />
They limit the influence of the previous iteration over the present one. If you choose small values it may prevent oscillations in residuum developing. At the same time the solution may need more time to converge. <br />
Keep the default values as they are given in FLUENT. You can decrease them gradually if necessary. Momentum 0.6, pressure 0.1, k 0.4, eps 0.4, mass source 1, viscosity 1.<br />
<br />
<br />
== Tips == <br />
==== How to merge two mesh files and make one? ====<br />
To merge two mesh files the suggested utility is tmerge. The syntax of tmerge is simple.<br><br />
<i>utility tmerge -3d file1 file2 finalfile </i> <br><br />
To join the two interior faces use: <br><br />
<i>Grid->Fuse</i> <br><br />
from the menu with Fluent.<br />
<br />
==== How to run multiple cases in batch mode ==== <br />
This could be achieved by running it from journal file. The example journal file that runs two cases is given as <br><br />
<i><br />
file read-case-data xxx1.cas <br><br />
solve dual-time-iterate yyy1 <br><br />
file write-case-data zzz1.cas <br><br />
file read-case-data xxx2.cas <br><br />
yes <b>(comment: for discard cas dialog) </b><br><br />
solve dual-time-iterate yyy2 <br><br />
file write-case-data zzz2.cas <br></i><br />
<br />
<br />
<br />
<br />
==== What does the abbreviation mean?====<br />
<br />
CFD = Computational Fluid dynamics<br />
FEM = Finite element model<br />
UDF = User defined function<br />
<br />
== FloWizard==<br />
<br />
== FIDAP==<br />
<br />
== POLYFLOW ==<br />
<br />
== Pre-processors ==<br />
<br />
=== Gambit ===<br />
<br />
=== Gambit Turbo ===<br />
<br />
=== TGrid ===<br />
<br />
== Application specific codes ==<br />
<br />
=== Icepak ===<br />
<br />
=== Airpak ===<br />
<br />
=== MixSim ===<br />
<br />
== Educational codes ==<br />
<br />
=== FlowLab ===<br />
<br />
<br />
[[Category: FAQ's]]<br />
<br />
{{stub}}</div>Zxaarhttp://www.cfd-online.com/Wiki/Fluent_FAQFluent FAQ2005-11-24T02:38:21Z<p>Zxaar: </p>
<hr />
<div>This section is empty. This is just a suggestion on how to structure it. Please feel free to add questions and answers here!<br />
<br />
== General purpose codes ==<br />
<br />
=== FLUENT ===<br />
== Solver Related ==<br />
==== What does the floating point error mean? How can I avoid it? ====<br />
<br />
The floating point error has been reported many times and discussed a lot. Here are some of the answers found in the Fluent Forum:<br />
<br />
'''SOLVER AND ITERATION''' -----I think if you set shorter time step, it may be good. Or changing little Under-Relaxiation-Factors, it may be good. In my experience, I set 1/3 Under-Relaxiation-Factors as default.� -----�also lower the values of under relaxation factor and use the coupled implicit solver� -----�Try to change under-relaxation factors and if it is unsteady problem maybe time step is to large.� -----�you can improve the ratio in the solve--control--limits, maybe that can help.� -----�you will need to decrease the Courant number� -----�If you still get the error, initialize the domain with nothing to 'Compute from...' Then click 'init'. Again select the surface from which you want to compute the initial values & iterate. This should work.� -----�Another reason could be a to high courant number - that means, that the steps between two iterations are too large and the change in the results is too large as well (high residuals)�<br />
<br />
'''GRID PROBLEMS''' -----�this error comes when I start scaling grid. in gambit, all my dimension is in mm, when in fluent i convert it in meter using buttone SCALE. after it, when i iterate, about hundred iteration, this error appeared. but when i not scale my drawing to m...and let it be as in gambit..then the iteration is success. -----�hi I think you should check your mesh grid mesh is very high. your problem solve by selection a low mesh.� -----�Your mesh is so heavy that your computers resources are not enough. try to use coarser mesh.�<br />
<br />
'''BOUNDARY CONDITIONS''' -----�In my case I had set a wall boundary condition instead of an axis boundary condition and then FLuent refuses to calculate telling me 'floating point error'.� -----�Your Boudary Conditions do not represent real physis.� -----�wrong boundary condition definition might cause the floating point error. For example setting an internal boundary as interior� -----�Once I had the problem, simulating a 2D chamber with a symmetry BC. I set the symmetry somewhere as �axe symmetric� and the floating point error occur� -----�check the turbulence parameter you set. reduce the turbulence intensity to less that one for first, say 50 iterations.<br />
<br />
'''USING A UDF''' -----�What I mean is really often when people creates UDF they generally forget that for the first iteration some variable can be zero. Therefore if you are divided a number by zero your solver will blow up telling you 'non floating error'. 'non' means 'not a number'. Depending on your UDF this kind of error does not effectively happens at the first iteration. An example, if you are simulated a domain with a stagnant water as initial condition and you are calculated for the first iteration something like 1/Re therefore lets call it BOOM !!! because Re=0 . To find this kind of think there a simple way : reread your UDF.�<br />
<br />
'''MULTI PROCESSOR ISSUES''' -----"I've had similar problems recently with floating point errors on a multi processor simulation. The solution for my problem seems to be to run on a single processor, where it runs fine....?�<br />
<br />
'''WRONG INITIATION''' ----- Initiating the case with wrong conditions may lead to floating point error when the iterations start.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Models Related ==<br />
==== What is the turbulent viscosity ratio warning and how can I handle? ====<br />
<br />
==== How can I determine the inputs for a porous media or porous jump from flow versus pressure drop data? ====<br />
<br />
==== How do I model heat conduction in a composite wall? ====<br />
<br />
==== What pressures should be specified at inlets and outlets for buoyancy flow problems? ====<br />
<br />
==== Are there any general guidelines on selecting a turbulence model? ====<br />
<br />
==== How can both turbulent and laminar flow be included in one model? ====<br />
<br />
==== How to start a 3D simulation with an compressible medium and temperature changes? What is important to consider ====<br />
<br />
<br />
<br />
== Solution Methodology == <br />
==== How do i carry out rotating body analysis, eg a rotating sphere or cylinder in flow? ====<br />
==== How do i get better and faster convergence? ====<br />
==== What is the role of under-relaxation parameters? What should be the optimum choice of these parameters? ====<br />
They limit the influence of the previous iteration over the present one. If you choose small values it may prevent oscillations in residuum developing. At the same time the solution may need more time to converge. <br />
Keep the default values as they are given in FLUENT. You can decrease them gradually if necessary. Momentum 0.6, pressure 0.1, k 0.4, eps 0.4, mass source 1, viscosity 1.<br />
<br />
<br />
== Tips == <br />
==== How to merge two mesh files and make one? ====<br />
To merge two mesh files the suggested utility is tmerge. The syntax of tmerge is simple.<br><br />
<i>utility tmerge -3d file1 file2 finalfile </i> <br><br />
To join the two interior faces use: <br><br />
<i>Grid->Fuse</i> <br><br />
from the menu with Fluent.<br />
<br />
==== How to run multiple cases in batch mode ==== <br />
This could be achieved by running it from journal file. The example journal file that runs two cases is given as <br><br />
<i><br />
file read-case-data xxx1.cas <br><br />
solve dual-time-iterate yyy1 <br><br />
file write-case-data zzz1.cas <br><br />
file read-case-data xxx2.cas <br><br />
yes <b>(comment: for discard cas dialog) </b><br><br />
solve dual-time-iterate yyy2 <br><br />
file write-case-data zzz2.cas <br></i><br />
<br />
<br />
<br />
<br />
==== What does the abbreviation mean?====<br />
<br />
CFD = Computational Fluid dynamics<br />
FEM = Finite element model<br />
UDF = User defined function<br />
<br />
== FloWizard==<br />
<br />
== FIDAP==<br />
<br />
== POLYFLOW ==<br />
<br />
== Pre-processors ==<br />
<br />
=== Gambit ===<br />
<br />
=== Gambit Turbo ===<br />
<br />
=== TGrid ===<br />
<br />
== Application specific codes ==<br />
<br />
=== Icepak ===<br />
<br />
=== Airpak ===<br />
<br />
=== MixSim ===<br />
<br />
== Educational codes ==<br />
<br />
=== FlowLab ===<br />
<br />
<br />
[[Category: FAQ's]]<br />
<br />
{{stub}}</div>Zxaarhttp://www.cfd-online.com/Wiki/Prandtl%27s_one-equation_modelPrandtl's one-equation model2005-11-24T02:02:37Z<p>Zxaar: </p>
<hr />
<div>==Kinematic Eddy Viscosity==<br />
:<math> <br />
\nu _t = k^{{1 \over 2}} l = C_D {{k^2 } \over \varepsilon }<br />
</math><br />
<br />
==Model==<br />
<br />
:<math><br />
{{\partial k} \over {\partial t}} + U_j {{\partial k} \over {\partial x_j }} = \tau _{ij} {{\partial U_i } \over {\partial x_j }} - C_D {{k^{{3 \over 2}} } \over l} + {\partial \over {\partial x_j }}\left[ {\left( {\nu + {{\nu _T } \over {\sigma _k }}} \right){{\partial k} \over {\partial x_j }}} \right]<br />
</math><br />
<br />
<br />
== Closure Coefficients and Auxilary Relations ==<br />
<br />
:<math><br />
\varepsilon = C_D {{k^{{3 \over 2}} } \over l}<br />
</math> <br><br />
:<math><br />
C_D = 0.3 <br />
</math> <br><br />
:<math><br />
\sigma _k = 1<br />
</math> <br><br />
<br />
<br />
where <br><br />
:<math><br />
\tau _{ij} = 2\nu _T S_{ij} - {2 \over 3}k\delta _{ij} <br />
</math><br />
<br />
== References ==<br />
<br />
#{{reference-book|author=Wilcox, D.C. |year=2004|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}}<br />
<br />
<br />
----<br />
<i> Return to [[Turbulence modeling]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Johnson-King_modelJohnson-King model2005-11-24T02:00:55Z<p>Zxaar: </p>
<hr />
<div>== References ==<br />
<br />
*<b>Johnson, D.A. and King, L.S.</b> A mathematically simple turbulence closure model for attached and separated turbulenc boundary layers, AIAA Journal, 23, 1684-1692, 1985.<br />
<br />
<br />
----<br />
<i> Return to [[Turbulence modeling]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Baldwin-Lomax_modelBaldwin-Lomax model2005-11-24T02:00:28Z<p>Zxaar: </p>
<hr />
<div>== Introduction ==<br />
<br />
The Baldwin-Lomax model is a two-layer algebraic 0-equation model which gives the eddy-viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace and turbomachinery applications. It is commonly used in quick design iterations where robustness is more important than capturing all details of the flow physics. The Baldwin-Lomax model is not suitable for cases with large separated regions and significant curvature/rotation effects (see below).<br />
<br />
<br />
== Equations ==<br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
\mu_t =<br />
\begin{cases}<br />
{\mu_t}_{inner} & \mbox{if } y \le y_{crossover} \\ <br />
{\mu_t}_{outer} & \mbox{if} y > y_{crossover}<br />
\end{cases}<br />
</math></td><td width="5%">(1)</td></tr></table><br />
<br />
Where <math>y_{crossover}</math> is the smallest distance from the surface where <math>{\mu_t}_{inner}</math> is equal to <math>{\mu_t}_{outer}</math>:<br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
y_{crossover} = MIN(y) \ : \ {\mu_t}_{inner} = {\mu_t}_{outer}<br />
</math></td><td width="5%">(2)</td></tr></table><br />
<br />
The inner region is given by the Prandtl - Van Driest formula:<br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
{\mu_t}_{inner} = \rho l^2 \left| \Omega \right|<br />
</math></td><td width="5%">(3)</td></tr></table><br />
<br />
Where<br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
l = k y \left( 1 - e^{\frac{-y^+}{A^+}} \right)<br />
</math></td><td width="5%">(4)</td></tr></table><br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
\left| \Omega \right| = \sqrt{2 \Omega_{ij} \Omega_{ij}}<br />
</math></td><td width="5%">(5)</td></tr></table><br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
\Omega_{ij} = \frac{1}{2}<br />
\left(<br />
\frac{\partial u_i}{\partial x_j} -<br />
\frac{\partial u_j}{\partial x_i}<br />
\right)<br />
</math></td><td width="5%">(6)</td></tr></table><br />
<br />
The outer region is given by:<br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
{\mu_t}_{outer} = \rho \, K \, C_{CP} \, F_{WAKE} \, F_{KLEB}(y)<br />
</math></td><td width="5%">(7)</td></tr></table><br />
<br />
Where<br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
F_{WAKE} = MIN \left( y_{MAX} \, F_{MAX} \,\,;\,\,<br />
C_{WK} \, y_{MAX} \, \frac{u^2_{DIF}}{F_{MAX}} \right)<br />
</math></td><td width="5%">(8)</td></tr></table><br />
<br />
<math>y_{MAX}</math> and <math>F_{MAX}</math> are determined from the maximum of the function:<br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
F(y) = y \left| \Omega \right| \left(1-e^{\frac{-y^+}{A^+}} \right)<br />
</math></td><td width="5%">(9)</td></tr></table><br />
<br />
<math>F_{KLEB}</math> is the intermittency factor given by:<br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
F_{KLEB}(y) = \left[1 + 5.5 \left( \frac{y \, C_{KLEB}}{y_{MAX}} \right)^6<br />
\right]^{-1}<br />
</math></td><td width="5%">(10)</td></tr></table><br />
<br />
<math>u_{DIF}</math> is the difference between maximum and minimum speed in the profile. For boundary layers the minimum is always set to zero.<br />
<br />
<table width="100%"><tr><td><br />
:<math><br />
u_{DIF} = MAX(\sqrt{u_i u_i}) - MIN(\sqrt{u_i u_i})<br />
</math></td><td width="5%">(11)</td></tr></table><br />
<br />
<br />
== Model constants ==<br />
<br />
The table below gives the model constants present in the formulas above. Note that <math>k</math> is a constant, and not the turbulence energy, as in other sections. It should also be pointed out that when using the Baldwin-Lomax model the turbulence energy, <math>k</math>, present in the governing equations, is set to zero.<br />
<br />
<table cellpadding="5" cellspacing="1" border="1"><br />
<tr><br />
<td><math>A^+</math></td><br />
<td><math>C_{CP}</math></td><br />
<td><math>C_{KLEB}</math></td><br />
<td><math>C_{WK}</math></td><br />
<td><math>k</math></td><br />
<td><math>K</math></td><br />
</tr><br />
<tr><br />
<td>26</td><br />
<td>1.6</td><br />
<td>0.3</td><br />
<td>0.25</td><br />
<td>0.4</td><br />
<td>0.0168</td><br />
</tr><br />
</table><br />
<br />
<br />
== Model variants ==<br />
<br />
In order to improve the Baldwin-Lomax model modifications of the model-constants can be made in order to account for the effect of adverse pressure gradients. This has been done by Granville and Turner and Jennions. For further information see the references below.<br />
<br />
<br />
== Performance, applicability and limitations ==<br />
<br />
The Baldwin-Lomax model is suitable for high-speed flows with thin attached boundary layers. Typical applications are aerospace and turbomachinery applications. It is a low-Re model and as such it requires a fairly well-resolved grid near the walls, with the first cell located at <math>y+ < 1</math>.<br />
<br />
The model is popular in quick design-iterations due to its robustness and reliability. It seldom leads to any convergence problems and it seldom gives completely unphysical results.<br />
<br />
The Baldwin-Lomax model should be used with great care in cases with large separations. It has been shown by several researchers that the Baldwin-Lomax model tends to overpredict separated regions (see for example the comments made by David Wilcox in his book Turbulence Modeling for CFD). However, there are ad-hoc modifications which reduce this problem. For instance, prediction of separation is sensitive to the value of the <math>C_{WK}</math> coefficient and higher values than the original value tend to reduce the problems with too early separation. Also note that the Granville correction mentioned above, which attempts to account for adverse pressure gradient effects, increases the problem with too large separations. <br />
<br />
The Baldwin-Lomax model does not account for the effect of a high free-stream turbulence level. Hence, it can not be used reliably when the free-stream turbulence has a signigicant effect on the boundary layer development.<br />
<br />
<br />
== Implementation issues ==<br />
<br />
''We need some further information here about what to think about when implementing this model in a CFD code. For example, there are some issues when computing the max and min values in the formulas - in complex 3D cases you can sometimes find several local mins/maxs. Can anyone add something about this?''<br />
<br />
<br />
== References ==<br />
<br />
* {{reference-paper|author=Baldwin, B. S. and Lomax, H.|year=1978|title=Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows|rest=AIAA Paper 78-257}}<br />
* {{reference-paper|author=Granville, P. S.|year=1987|title=Baldwin-Lomax Factors for Turbulent Boundary Layers in Pressure Gradients|rest=AIAA Journal, Vol. 25, No. 12, pp. 1624-1627}}<br />
* {{reference-paper|author=Turner, M. G. and Jennions, I. K.|year=1993|title=An Investigation of Turbulence Modeling in Transonic Fans Including a Novel Implementation of an Implicit <math>k-\epsilon</math> Turbulence Model|rest=Journal of Turbomachinery, Vol. 115, April, pp. 249-260}}<br />
<br />
<br />
----<br />
<i> Return to [[Turbulence modeling]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Cebeci-Smith_modelCebeci-Smith model2005-11-24T02:00:07Z<p>Zxaar: </p>
<hr />
<div>== References ==<br />
<br />
*<b>Smith, A.M.O. and Cebeci, T.</b> Numerical solution of the turbulent boundary layer equations, Douglas aircraft division report DAC 33735.<br />
<br />
<br />
----<br />
<i> Return to [[Turbulence modeling]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Algebraic_turbulence_modelsAlgebraic turbulence models2005-11-24T01:59:48Z<p>Zxaar: </p>
<hr />
<div><br />
<br />
----<br />
<i> Return to [[Turbulence modeling]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Introduction_to_turbulenceIntroduction to turbulence2005-11-24T01:59:23Z<p>Zxaar: </p>
<hr />
<div>==What is Turbulence?==<br />
<br />
Turbulence is that state of fluid motion which is characterized by apparently random and chaotic three-dimensional [[vorticity]]. When turbulence is present, it usually dominates all other flow phenomena and results in increased energy dissipation, mixing, heat transfer, and drag.<br />
<br />
For a long time scientists were not really sure in which sense turbulence is 'random', but they were pretty sure it was. Like any one who is trained in physics, we believe the flows we see around us must be the solution to some set of equations which govern. (This is after all what mechanics is about- writing equations to describe and predict the world around us) But because of the nature of the turbulence, it wasn't clear whether the equations themselves had some hidden randomness, or just the solutions. And if the latter, was it something the equations did to them, or a consequence of the intial conditions<br />
<br />
===Why Study Turbulence?===<br />
<br />
There really are the two reasons for studying turbulence- engineering and physics! And they are not necessarily complementary, atleast in the short run.<br />
<br />
Certainly a case can be made that we don't know enough about the turbulence to even start to consider engineering problems. To begin with, we always have fewer equations that unknowns in any attempt to predict anything other than the instantaneous motions. This is the famous [[turbulence closure problem]].<br />
<br />
Of course, closure is not a problem when performing a [[Direct numerical simulation (DNS)| direct numerical simulation]] in which we numerically produce the instantaneous motions in a computer using the exact equations governing the fluid. Unfortunately we won't be able to perform such simulations for real engineering problems until at least a few hundred generations of computers have come and gone. And this won't really help us too much, since even when we now perform a DNS simulation of a really simple flow, we are already overwhelmed by the amount of data and its apparent random behaviour. This is because without some kind of theory, we have no criteria for selecting from it in a single lifetime what is important.<br />
<br />
The engineer's counter argument to the scientist's lament above is:<br />
<br />
* airplanes must fly,<br />
* weather must be forecast,<br />
* sewage and water management systems must be built<br />
* society needs ever more energy-efficient hardware and gadgets.<br />
<br />
Thus the engineer argues, no matter the inadequate state of our knowledge, '''we have the responsibilty as engineers to do the best we can with what we have'''. Who, considering the needs, could seriously argue with this? Almost incredibly - some physicists do!<br />
<br />
It seems evindent then that there must be at least two levels of assault on turbulence. At one level, the very nature of turbulence must be explored. At the other level, our current state of knowledge- however inadequate it might be- must be stretched to provide engineering solutions to real problems.<br />
<br />
===The cost of our ignorance===<br />
<br />
It is difficult to place a price tag on the cost of our limited understanding of turbulence, but it requires no imagination at all to realize that it must be enormous. Try to estimate, for example, the aggregate cost to society of our limited turbulence prediction abilities which result in inadequate weather-forecasts alone. Or try to place a value on the increased cost to the consumer need of the designer of virtually every fluid-thermal system-from heat exchangers to hypersonic planes- to depend on empiricism and experimentation, with the resulting need for abundant safety factors and non-optimal performance by all but the crudest measures.Or consider the frustration to engineers and cost to management of the never-ending need for 'code-validation' experiments every time a new class of flows is encounteredor major design change is contemplated. The whole idea of 'codes' in the first place was to be able to evaluate designs wihtout having to do experiments or build prototypes.<br />
<br />
===What do we really know for sure?===<br />
<br />
Turbulence is a subject on which still studies are going on. We really don't know a whole lot for sure about turbulence. And worse, we even disagree about what we think we know! There are indeed some things some researchers think we understand pretty well - like for example the kolmogorov similarity theory for the dissipative scales and the Law of the Wall for wall-bounded flows. These are based on assumptions and logical constructions about how we believe turbulence behaves in the limit of infinite Reynolds number. But even these ideas have never been tested in controlled laboratory experiments in the limits of high Reynolds number, because no one has ever had the large scale facilities required to do so.<br />
<br />
It seems to be a characteristic of humans(and contrary to popular beleif, scientists and engineers are indeed human) that we tend to accept ideas which have been around a while as fact, instead of just working hypotheses that are still waiting to be tested. One can reasonably argue that the acceptance of most ideas in turbulence is perhaps more due to the time lapsed since they were proposed and found to be in resonable agreement with limited data base, than that they have been subjected to experimental tests over the range of their assumed validity. Thus it might be wise to view most 'established' laws and theories of turbulence as more like religious creeds than matters of fact.<br />
<br />
The whole situation is a bit analogous to the old idea that the sun and stars revolved around the earth - it was a fine idea, and even good today for navigational purposes. The only problem was that one day someone (Copernicus, Brahe and Galileo among them) looked up and realized it wasn't true. So it may be with a lot of what we believe today to be true about turbulence - some day you may be the one to look at evidence in a new way and decide that things we thought to be true are wrong.<br />
<br />
==The Reynolds Averaged Equations and the Turbulence Closure Problem==<br />
<br />
=== The Equations Governing the Instantaneous Fluid Motions ===<br />
<br />
All fluid motions, whether turbulent or not, are governed by the dynamical equations for a fluid. These can be written using Cartesian tensor notation as:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\rho\left[\frac{\partial \tilde{u}_i}{\partial t}+\tilde{u}_j\frac{\partial \tilde{u}_i}{\partial x_j}\right] = -\frac{\partial \tilde{p}}{\partial x_i}+\frac{\partial \tilde{T}_{ij}^{(v)}}{\partial x_j}</math><br />
</td><td width="5%">(2.1)</td></tr></table><br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\left[\frac{\partial \tilde{\rho}}{\partial t}+\tilde{u}_j\frac{\partial \tilde{\rho}}{\partial x_j}\right]+ \tilde{\rho}\frac{\partial \tilde{u}_j}{\partial x_j}= 0 </math><br />
</td><td width="5%">(2.2)</td></tr></table><br />
<br />
<br />
where <math>\tilde{u_i}(\vec{x},t)</math> represents the i-the component of the fluid velocity at a point in space,<math>[\vec{x}]_i=x_i</math>, and time,t. Also <br />
<math>\tilde{p}(\vec{x},t)</math> represents the static pressure, <math>\tilde{T}_{ij}^{(v)}(\vec{x},t)</math>, the viscous(or deviatoric) stresses, and <math>\tilde\rho</math> the fluid density. The tilde over the symbol indicates that an instantaneous quantity is being considered. Also the Einstein summation convention has been employed[1].<br />
<br />
In equation 2.1, the subscript i is a free index which can take on the values 1,2 and 3. Thus equation 2.1 is in reality three separate equations. These three equations are just Newton's second law written for a continuum in a spatial(or Eulerian) reference frame. Together they relate the rate of change of momentum per unit mass <math>(\rho{u_i})</math>,a vector quantity, to the contact and body forces.<br />
<br />
Equation 2.2 is the equation for mass conservation in the absence of sources(or sinks) of mass. Almost all flows considered in this material will be incompressible, which implies that derivative of the density following the fluid material[the term in brackets] is zero. Thus for incompressible flows, the mass conservation equation reduces to:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\frac{D \tilde{\rho}}{Dt}=\frac{\partial \tilde{\rho}}{\partial t}+\tilde{u}_j\frac{\partial \tilde{\rho}}{\partial x_j}= 0</math><br />
</td><td width="5%">(2.3)</td></tr></table><br />
<br />
From equation 2.2 it follows that for incompressible flows,<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\frac{\partial \tilde{u}_i}{\partial x_j}= 0</math><br />
</td><td width="5%">(2.4)</td></tr></table><br />
<br />
The viscous stresses(the stress minus the mean normal stress) are represented by the tensor<math>\tilde{T}_{ij}^{(v)}</math>. From its definition,<math>\tilde{T}_{kk}^{(v)}</math>=0. In many flows of interest, the fluid behaves as a Newtonian fluid in which the viscous stress can be related to the fluid motion by a constitutive relation of the form.<br />
<br />
<table width="100%"><br />
<tr><td><br />
<math>\tilde{T}_{ij}^{(v)}= 2\mu[\tilde{s}_{ij}-\frac{1}{3}\tilde{s}_{kk}\delta_{ij}] </math><br />
</td><td width="5%">(2.5)</td></tr></table><br />
<br />
The viscosity, <math>\mu</math>, is a property of the fluid that can be measured in an independent experiment. <math>\tilde s_{ij}</math> is the instantaneous strain rate tensor defined by<br />
<br />
<table width="100%"><br />
<tr><td><br />
<math>\tilde{s}_{ij}= \frac{1}{2}\left[\frac{\partial \tilde u_i}{\partial x_j}+\frac{\partial \tilde u_j}{\partial x_i}\right] </math><br />
</td><td width="5%">(2.6)</td></tr></table><br />
<br />
From its definition, <math>\tilde s_{kk}=\frac{\partial \tilde u_k}{\partial x_k}</math>. If the flow is incompressible, <math>\tilde s_{kk}=0</math> and the Newtonian constitutive equation reduces to<br />
<table width="100%"><br />
<tr><td><br />
<math>\tilde{T}_{ij}^{(v)}= 2\mu\tilde{s}_{ij}</math><br />
</td><td width="5%">(2.7)</td></tr></table><br />
<br />
Throughout this material, unless explicitly stated otherwise, the density <math>\tilde\rho=\rho</math> and the viscosity <math>\mu</math> will be assumed constant. With these assumptions, the instantaneous momentum equations for a Newtonian Fluid reduce to:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\left[\frac{\partial \tilde{u}_i}{\partial t}+\tilde{u}_j\frac{\partial \tilde{u}_i}{\partial x_j}\right] = -\frac {1}{\tilde\rho}\frac{\partial \tilde{p}}{\partial x_i}+\nu\frac{\partial^2 {\tilde{u}_i}}{\partial x_j^2}</math><br />
</td><td width="5%">(2.8)</td></tr></table><br />
<br />
where the kinematic viscosity, <math>\nu</math>, has been defined as:<br />
<table width="100%"><br />
<tr><td><br />
<math>\nu\equiv\frac{\mu}{\rho}</math><br />
</td><td width="5%">(2.9)</td></tr></table><br />
<br />
Note that since the density is assumed conastant, the tilde is no longer necessary.<br />
<br />
Sometimes it will be more instructive and convenient to not explicitly include incompressibilty in the stress term, but to refer to the incompressible momentum equation in the following form:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\rho\left[\frac{\partial \tilde{u}_i}{\partial t}+\tilde{u}_j\frac{\partial \tilde{u}_i}{\partial x_j}\right] = -\frac{\partial \tilde{p}}{\partial x_i}+\frac{\partial \tilde{T}_{ij}^{(v)}}{\partial x_j}</math><br />
</td><td width="5%">(2.10)</td></tr></table><br />
<br />
This form has the advantage that it is easier to keep track of the exact role of the viscous stresses.<br />
<br />
=== Equations for the Average Velocity ===<br />
<br />
<br />
Although laminar solutions to the equations often exist that are consistent with the boundary conditions, perturbations to these solutions(sometimes even infinitesimal) can cause them to become turbulent. To see how this can happen, it is convenient to analyze the flow in two parts, a mean(or average) component and a fluctuating component. Thus the instantaneous velocity and stresses can be written as:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\tilde {u}_i=U_i+u_i<br />
</math><br />
:<math><br />
\tilde p=P+p<br />
</math><br />
:<math><br />
\tilde T_{ij}^{(v)}=T_{ij}^{(v)}+\tau_{ij}^{(v)}<br />
</math><br />
</td><td width="5%">(2.11)</td></tr><br />
</table><br />
<br />
<br />
Where <math>U_i</math>, <math>P</math> and <math>T_{ij}^{(v)}</math> represent the mean motion, and <math>u_i</math>, <math>p</math> and <math>\tau_{ij}^{(v)}</math> the fluctuating motions. This technique for decomposing the instantaneous motion is referred to as the '''''Reynolds decomposition.''''' Note that if the averages are defined as ensemble means, they are, in general, time-dependent. For the remainder of this material unless other wise stated, the density will be assumed constant so<math>\tilde{\rho}\equiv\rho</math>,and its fluctuation is zero.<br />
<br />
Substitution of equations 2.11 into equations 2.10 yields<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\rho\left[\frac{\partial (U_i+u_i)}{\partial t}+(U_j+u_j)\frac{\partial (U_i+u_i)}{\partial x_j}\right] = -\frac{\partial (P+p)}{\partial x_i}+\frac{\partial (T_{ij}^{(v)}+\tau_{ij}^{(v)})}{\partial x_j}</math><br />
</td><td width="5%">(2.12)</td></tr></table><br />
<br />
This equation can now be averaged to yield an equation expressing momentum conservation for the averaged motion. Note that the operations of averaging and differentiation commute; i.e., the average of a derivative is the same as the derivative of the average. Also the average of a fluctuating quantity is zero. Thus the equation for the averaged motion reduces to:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\rho\left[\frac{\partial U_i}{\partial t}+U_j\frac{\partial U_i}{\partial x_j}\right] = -\frac{\partial P}{\partial x_i}+\frac{\partial T_{ij}^{(v)}}{\partial x_j}-\rho\left \langle u_j\frac{\partial u_i }{\partial x_j} \right \rangle</math><br />
</td><td width="5%">(2.13)</td></tr></table><br />
<br />
where the remaining fluctuating product term has been moved to the right hand side of the equation. Whether or not the last term is zero like the other fluctuating term depends on the correlation of the terms in the product. In general, these correlations are not zero.<br />
<br />
The mass conservation equation can be similarly decomposed. In incompressible form, substitution of equations 2.11 into equation 2.4 yields:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\frac{\partial (U_j+u_j)}{\partial x_j}=0</math><br />
</td><td width="5%">(2.14)</td></tr></table><br />
<br />
of which average is <br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\frac{\partial U_j}{\partial x_j}=0</math><br />
</td><td width="5%">(2.15)</td></tr></table><br />
<br />
It is clear from the equation 2.15 that the averaged motion satisfies the same form of the mass conservation equation as does the instantaneous motion at least for incompressible flows. How much simpler the turbulence problem would be if the same were true for the momentum! Unfortunately, as is easily seen from the equation 2.13, such is not the case.<br />
<br />
Equation 2.15 can be subtracted from equation 2.14 to yield an equation for instantaneous motion alone; i.e,<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\frac{\partial u_j}{\partial x_j}=0</math><br />
</td><td width="5%">(2.16)</td></tr></table><br />
<br />
Again, like the mean, the form of the original instantaneous equation is seen to be preserved. The reason, of course, is obvious: the continuity equation is linear. The momentum equation , on the other hand, is not; hence the difference.<br />
<br />
Equation 2.16 can be used to rewrite the last term in equation 2.13 for the mean momentum. Multiplying equation 2.16 by <math>u_i</math> and averaging yields:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\left \langle u_i\frac{\partial u_j}{\partial x_j}\right \rangle=0</math><br />
</td><td width="5%">(2.17)</td></tr></table><br />
<br />
This can be added to:<math>\left \langle u_j\frac{\partial u_i}{\partial x_j}\right \rangle</math> to obtain:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\left \langle u_j\frac{\partial u_i}{\partial x_j}\right \rangle +0=\left \langle u_j\frac{\partial u_i}{\partial x_j}\right \rangle+ \left \langle u_i\frac{\partial u_j}{\partial x_j}\right \rangle =\frac{ \partial}{\partial x_j}{\left \langle u_iu_j\right \rangle} </math><br />
</td><td width="5%">(2.18)</td></tr></table><br />
<br />
Where again the fact that arithmetic and averaging operations commute has been used.<br />
<br />
The equation for the averaged momentum, equation 2.13 can now be rewritten as:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\rho\left[\frac{\partial U_i}{\partial t}+U_j\frac{\partial U_i}{\partial x_j}\right] = -\frac{\partial P}{\partial x_i}+\frac{\partial T_{ij}^{(v)}}{\partial x_j}-\frac{ \partial}{\partial x_j}{(\rho\left \langle u_iu_j\right \rangle)}</math><br />
</td><td width="5%">(2.19)</td></tr></table><br />
<br />
The last two terms on the right hand side are both divergence terms and can be combined; the result is:<br />
<br />
<table width="100%"><br />
<tr><td><br />
:<math><br />
\rho\left[\frac{\partial U_i}{\partial t}+U_j\frac{\partial U_i}{\partial x_j}\right] = -\frac{\partial P}{\partial x_i}+\frac{\partial }{\partial x_j}[T_{ij}^{(v)}-{\rho\left \langle u_iu_j\right \rangle}]</math><br />
</td><td width="5%">(2.20)</td></tr></table><br />
<br />
Now the terms in square brackets on the right have the dimensions of stress. The first term is, in fact , the viscous stress. The second term, on the other hand, is not a stress at all, but simply a re-worked version of the fluctuating contribution to the non-linear acceleration terms. The fact that it can be written this way, however, indicates that at least as far as the motion is concerned, it acts as though it were a stress- hence its name, the '''Reynolds stress'''. In the succeeding sections the consequences of this difference will be examined.<br />
<br />
=== The Turbulence Problem ===<br />
<br />
It is the appearance of the Reynolds stress which makes the turbulence problem so difficult - at least from the engineers perspective. Even though we can pretend it is a stress, the physics which give rise to it are very different from the viscous stress. The viscous stress can be related directly to the other flow properties by constitutive equations, which in turn depend only on the properties of the fluid( as in equation 2.5 for a Newtonian fluid). The reason this works is that when we make such closure approximations for a fluid, we are averaging over characteristic length and time scales much smaller than those of the flows we are interested in. Yet at the same time, these scales are much larger than the molecular length and time scales which characterize the molecular interactions that are actually causing the momentum transfer. (This is what the continuum approximation is all about).<br />
<br />
The '''''Reynolds stress''''', on the other hand, arises from the flow itself! Worse, the scales of the fluctuating motion which give rise to it are the scales we are interested in. This means that the closure ideas which worked so well for the viscous stress, should not be expected to work too well for the Reynolds stress. And as we shall see, they do not.<br />
<br />
This leaves us in a terrible position. Physics and engineering are all about writing equations(and boundary conditions) so we can solve them to make predictions. We don't want to have a build prototype airplanes first to see if they will they fall out of the sky. Instead we want to be able to analyze our designs before building, to save the cost in money and lives if our ideas are wrong. The same is true for dams and bridges and tunnels and automobiles. If we had confidence in our turbulence models, we could even build huge one-offs and expect them to work the first time. Unfortunately, even though turbulence models have improved to the point where we can use them in design, we still cannot trust them enough to eliminate expensive wind tunnel and model studies. And recent history is full of examples to prove this.<br />
<br />
The turbulence problem (from the engineers perspective) is then three-fold:<br />
<br />
* '''The averaged equations are not closed.''' Count the number of unknowns in equation 2.20 above. Then count the number of equations. Even with the continuity equation we have atleast six equations too few.<br />
<br />
* '''The simple ideas to provide the extra equations usually do not work.''' And even when we can fix them up for a particular class of flows (like the flow in a pipe, for example), they will most likely not be able to predict what happens in even a slightly different environment(like a bend).<br />
<br />
*'''Even the last resort of compiling engineering tables for design handbooks carries substantial risk.''' This is the last resort for the engineer who lacks equations or cannot trust them. Even when based on a wealth of experience, they require expensive model testing to see if they can be extrapolated to a particular situation. Often they cannot, so infinitely clever is Mother Nature in creating turbulence that is unique to a particular set of boundary conditions.<br />
<br />
'''Turbulent flows are indeed flows!'''. And that is the problem.<br />
<br />
==2.4 The Origins of Turbulence==<br />
<br />
Turbulent flows can often be observed to arise from laminar flows as the Reynolds number, (or someother relevant parameter) is increased. This happens because small disturbances to the flow are no longer damped by the flow, but begin to grow by taking energy from the original laminar flow. This natural process is easily visualized by watching the simple stream of water from a faucet (or even a pitcher). Turn the flow on very slow (or pour) so the stream is very smooth initially, at least near the outlet. Now slowly open the faucet (or pour faster) abd observe what happens, first far away, then closer to the spout. The surface begins to exhibit waves or ripples which appear to grow downstream . In fact, they are growing by extracting energy from the primary flow. Eventually they grow enough that the flow breaks into drops. These are capillary instabilities arisiing from surface tension, but regardless of the type of instability, the idea is the same -small (or infinitesimal ) disturbances have grown to disrupt the serenity (and simplicity) of laminar flow.<br />
<br />
The manner in which the instabilities grow naturally in a flow can be examined using the equations we have already developed above. We derived them by decomposing the motion into a mean and fluctuating part. But suppose instead we had decomposed the motion into a base flow part (the initial laminar part) and into a disturbance which represents a fluctuating part superimposed on the base flow. The result of substituting such a decomposition into the full Navier-Stokes equations and averaging is precisely that given by equations 2.13 and 2.15. But the very important difference is the additional restriction that what was previously identified as the mean (or averaged ) motion is now also the base or laminar flow.<br />
<br />
Now if the base flow is really laminar flow (which it must be by our original hypothesis), then our averaged equations governing the base flow must yield the same mean flow as the original laminar flow on which the disturbances was superimposed. But this can happen only if these new averaged equations reduce to '''exactly''' the same lamiane flow equations without any evidence of a disturbance. Clearly from equations 2.13 and 2.15, this can happen ''only if all the Reynolds stress terms vanish identically!'' Obviously this requires that the disturbances be infintesimal so the extra terms can be neglected - hence our interest in infinitesimal disturbances.<br />
<br />
So we hypothesized a base flow which was laminar and showed that it is unchanged even with the imposition of infintesimal disturbances on it - ''but only as long as the disturbances'' '''remain''' ''infinitesimal!'' What happens if the disturbance starts to grow? Obviously before we conclude that all laminar flows are laminar forever we better investigate whether or not these infinitesimal disturbances can grow to ''finite'' size. To do this we need an equation for the fluctuation itself.<br />
<br />
more to come soon.............<br />
<br />
==Credits==<br />
'''This text was based on "Introduction to Turbulence" by Professor William K.George, Chalmers University of Technology, Sweden.'''<br />
<br />
<br />
----<br />
<i> Return to [[Turbulence modeling]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Runge_Kutta_methodsRunge Kutta methods2005-11-24T01:11:35Z<p>Zxaar: </p>
<hr />
<div>Runge Kutta (RK) methods are an important class of methods for integrating initial value problems formed by [[ODE]]s. Runge Kutta methods encompass a wide selection of numerical methods and some commonly used methods such as Explicit or Implicit [[Euler method]], the implicit midpoint rule and the trapezoidal rule are actually simplified versions of a general RK method.<br />
<br />
For the ODE,<br />
<br />
:<math><br />
y^\prime = f(t,y)<br />
</math><br />
<br />
the basic idea is to build a series of "stages", <math>k_i</math> that approximate the solution <math>y</math> at various points using samples of <math>f</math> from other stages. Finally, the numerical solution <math>u_{n+1}</math> is constructed from a linear combination of <math>u_n</math> and all the precomputed stages.<br />
<br />
Since the computation of one stage may involve other stages <math>k_i</math> the right hand side <math>f</math> is evaluated in a complicated nonlinear way. The most famous classical RK scheme is described below.<br />
<br />
= Fourth order Runge-Kutta method =<br />
<br />
The fourth order Runge-Kutta method could be summarized as:<br />
<br />
==Algorithm==<br />
::<math>y^\prime = f\left( {t,y} \right) </math><br />
::<math>k_1 = hf\left( {t_n ,y_n } \right) </math><br />
::<math>k_2 = hf\left( {t_n + {h \over 2},y_n + {{k_1 } \over 2}} \right) </math><br />
::<math>k_3 = hf\left( {t_n + {h \over 2},y_n + {{k_2 } \over 2}} \right) </math><br />
::<math>k_4 = hf\left( {t_n + h,y_n + k_3 } \right) </math><br />
::<math>y_{n + 1} = y_n + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6} </math><br />
<br />
<br />
<br />
{{stub}} <br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Runge_Kutta_methodsRunge Kutta methods2005-11-24T01:10:48Z<p>Zxaar: </p>
<hr />
<div>Runge Kutta (RK) methods are an important class of methods for integrating initial value problems formed by [[ODE]]s. Runge Kutta methods encompass a wide selection of numerical methods and some commonly used methods such as Explicit or Implicit [[Euler Method]], the implicit midpoint rule and the trapezoidal rule are actually simplified versions of a general RK method.<br />
<br />
For the ODE,<br />
<br />
:<math><br />
y^\prime = f(t,y)<br />
</math><br />
<br />
the basic idea is to build a series of "stages", <math>k_i</math> that approximate the solution <math>y</math> at various points using samples of <math>f</math> from other stages. Finally, the numerical solution <math>u_{n+1}</math> is constructed from a linear combination of <math>u_n</math> and all the precomputed stages.<br />
<br />
Since the computation of one stage may involve other stages <math>k_i</math> the right hand side <math>f</math> is evaluated in a complicated nonlinear way. The most famous classical RK scheme is described below.<br />
<br />
= Fourth order Runge-Kutta method =<br />
<br />
The fourth order Runge-Kutta method could be summarized as:<br />
<br />
==Algorithm==<br />
::<math>y^\prime = f\left( {t,y} \right) </math><br />
::<math>k_1 = hf\left( {t_n ,y_n } \right) </math><br />
::<math>k_2 = hf\left( {t_n + {h \over 2},y_n + {{k_1 } \over 2}} \right) </math><br />
::<math>k_3 = hf\left( {t_n + {h \over 2},y_n + {{k_2 } \over 2}} \right) </math><br />
::<math>k_4 = hf\left( {t_n + h,y_n + k_3 } \right) </math><br />
::<math>y_{n + 1} = y_n + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6} </math><br />
<br />
<br />
<br />
{{stub}} <br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Fluent_FAQFluent FAQ2005-11-24T01:08:40Z<p>Zxaar: </p>
<hr />
<div>This section is empty. This is just a suggestion on how to structure it. Please feel free to add questions and answers here!<br />
<br />
== General purpose codes ==<br />
<br />
=== FLUENT ===<br />
== Solver Related ==<br />
==== What does the floating point error mean? How can I avoid it? ====<br />
<br />
The floating point error has been reported many times and discussed a lot. Here are some of the answers found in the Fluent Forum:<br />
<br />
'''SOLVER AND ITERATION''' -----I think if you set shorter time step, it may be good. Or changing little Under-Relaxiation-Factors, it may be good. In my experience, I set 1/3 Under-Relaxiation-Factors as default.� -----�also lower the values of under relaxation factor and use the coupled implicit solver� -----�Try to change under-relaxation factors and if it is unsteady problem maybe time step is to large.� -----�you can improve the ratio in the solve--control--limits, maybe that can help.� -----�you will need to decrease the Courant number� -----�If you still get the error, initialize the domain with nothing to 'Compute from...' Then click 'init'. Again select the surface from which you want to compute the initial values & iterate. This should work.� -----�Another reason could be a to high courant number - that means, that the steps between two iterations are too large and the change in the results is too large as well (high residuals)�<br />
<br />
'''GRID PROBLEMS''' -----�this error comes when I start scaling grid. in gambit, all my dimension is in mm, when in fluent i convert it in meter using buttone SCALE. after it, when i iterate, about hundred iteration, this error appeared. but when i not scale my drawing to m...and let it be as in gambit..then the iteration is success. -----�hi I think you should check your mesh grid mesh is very high. your problem solve by selection a low mesh.� -----�Your mesh is so heavy that your computers resources are not enough. try to use coarser mesh.�<br />
<br />
'''BOUNDARY CONDITIONS''' -----�In my case I had set a wall boundary condition instead of an axis boundary condition and then FLuent refuses to calculate telling me 'floating point error'.� -----�Your Boudary Conditions do not represent real physis.� -----�wrong boundary condition definition might cause the floating point error. For example setting an internal boundary as interior� -----�Once I had the problem, simulating a 2D chamber with a symmetry BC. I set the symmetry somewhere as �axe symmetric� and the floating point error occur� -----�check the turbulence parameter you set. reduce the turbulence intensity to less that one for first, say 50 iterations.<br />
<br />
'''USING A UDF''' -----�What I mean is really often when people creates UDF they generally forget that for the first iteration some variable can be zero. Therefore if you are divided a number by zero your solver will blow up telling you 'non floating error'. 'non' means 'not a number'. Depending on your UDF this kind of error does not effectively happens at the first iteration. An example, if you are simulated a domain with a stagnant water as initial condition and you are calculated for the first iteration something like 1/Re therefore lets call it BOOM !!! because Re=0 . To find this kind of think there a simple way : reread your UDF.�<br />
<br />
'''MULTI PROCESSOR ISSUES''' -----"I've had similar problems recently with floating point errors on a multi processor simulation. The solution for my problem seems to be to run on a single processor, where it runs fine....?�<br />
<br />
'''WRONG INITIATION''' ----- Initiating the case with wrong conditions may lead to floating point error when the iterations start.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Models Related ==<br />
==== What is the turbulent viscosity ratio warning and how can I handle? ====<br />
<br />
==== How can I determine the inputs for a porous media or porous jump from flow versus pressure drop data? ====<br />
<br />
==== How do I model heat conduction in a composite wall? ====<br />
<br />
==== What pressures should be specified at inlets and outlets for buoyancy flow problems? ====<br />
<br />
==== Are there any general guidelines on selecting a turbulence model? ====<br />
<br />
==== How can both turbulent and laminar flow be included in one model? ====<br />
<br />
==== How to start a 3D simulation with an compressible medium and temperature changes? What is important to consider ====<br />
<br />
<br />
<br />
== Solution Methodology == <br />
==== How do i carry out rotating body analysis, eg a rotating sphere or cylinder in flow? ====<br />
==== How do i get better and faster convergence? ====<br />
==== What is the role of under-relaxation parameters? What should be the optimum choice of these parameters? ====<br />
They limit the influence of the previous iteration over the present one. If you choose small values it may prevent oscillations in residuum developing. At the same time the solution may need more time to converge. <br />
Keep the default values as they are given in FLUENT. You can decrease them gradually if necessary. Momentum 0.6, pressure 0.1, k 0.4, eps 0.4, mass source 1, viscosity 1.<br />
<br />
<br />
== Tips == <br />
==== How to merge two mesh files and make one? ====<br />
To merge two mesh files the suggested utility is tmerge. The syntax of tmerge is simple.<br><br />
<i>utility tmerge -3d file1 file2 finalfile </i> <br><br />
To join the two interior faces use: <br><br />
<i>Grid->Fuse</i> <br><br />
from the menu with Fluent.<br />
<br />
==== How to run multiple cases in batch mode ==== <br />
This could be achieved by running it from journal file. The example journal file that runs two cases is given as <br><br />
<i><br />
file read-case-data xxx1.cas <br><br />
solve dual-time-iterate yyy1 <br><br />
file write-case-data zzz1.cas <br><br />
file read-case-data xxx2.cas <br><br />
yes <b>(comment: for discard cas dialog) </b><br><br />
solve dual-time-iterate yyy2 <br><br />
file write-case-data zzz2.cas <br></i><br />
<br />
<br />
<br />
<br />
==== What does the abbreviation mean?====<br />
<br />
CFD = Computational Fluid dynamics<br />
FEM = Finite element model<br />
UDF = User defined function<br />
<br />
=== FloWizard ===<br />
<br />
=== FIDAP ===<br />
<br />
=== POLYFLOW ===<br />
<br />
== Pre-processors ==<br />
<br />
=== Gambit ===<br />
<br />
=== Gambit Turbo ===<br />
<br />
=== TGrid ===<br />
<br />
== Application specific codes ==<br />
<br />
=== Icepak ===<br />
<br />
=== Airpak ===<br />
<br />
=== MixSim ===<br />
<br />
== Educational codes ==<br />
<br />
=== FlowLab ===<br />
<br />
<br />
[[Category: FAQ's]]<br />
<br />
{{stub}}</div>Zxaarhttp://www.cfd-online.com/Wiki/Fluent_FAQFluent FAQ2005-11-24T01:03:32Z<p>Zxaar: </p>
<hr />
<div>This section is empty. This is just a suggestion on how to structure it. Please feel free to add questions and answers here!<br />
<br />
== General purpose codes ==<br />
<br />
=== FLUENT ===<br />
<br />
<br />
==== What does the floating point error mean? How can I avoid it? ====<br />
<br />
The floating point error has been reported many times and discussed a lot. Here are some of the answers found in the Fluent Forum:<br />
<br />
'''SOLVER AND ITERATION''' -----I think if you set shorter time step, it may be good. Or changing little Under-Relaxiation-Factors, it may be good. In my experience, I set 1/3 Under-Relaxiation-Factors as default.� -----�also lower the values of under relaxation factor and use the coupled implicit solver� -----�Try to change under-relaxation factors and if it is unsteady problem maybe time step is to large.� -----�you can improve the ratio in the solve--control--limits, maybe that can help.� -----�you will need to decrease the Courant number� -----�If you still get the error, initialize the domain with nothing to 'Compute from...' Then click 'init'. Again select the surface from which you want to compute the initial values & iterate. This should work.� -----�Another reason could be a to high courant number - that means, that the steps between two iterations are too large and the change in the results is too large as well (high residuals)�<br />
<br />
'''GRID PROBLEMS''' -----�this error comes when I start scaling grid. in gambit, all my dimension is in mm, when in fluent i convert it in meter using buttone SCALE. after it, when i iterate, about hundred iteration, this error appeared. but when i not scale my drawing to m...and let it be as in gambit..then the iteration is success. -----�hi I think you should check your mesh grid mesh is very high. your problem solve by selection a low mesh.� -----�Your mesh is so heavy that your computers resources are not enough. try to use coarser mesh.�<br />
<br />
'''BOUNDARY CONDITIONS''' -----�In my case I had set a wall boundary condition instead of an axis boundary condition and then FLuent refuses to calculate telling me 'floating point error'.� -----�Your Boudary Conditions do not represent real physis.� -----�wrong boundary condition definition might cause the floating point error. For example setting an internal boundary as interior� -----�Once I had the problem, simulating a 2D chamber with a symmetry BC. I set the symmetry somewhere as �axe symmetric� and the floating point error occur� -----�check the turbulence parameter you set. reduce the turbulence intensity to less that one for first, say 50 iterations.<br />
<br />
'''USING A UDF''' -----�What I mean is really often when people creates UDF they generally forget that for the first iteration some variable can be zero. Therefore if you are divided a number by zero your solver will blow up telling you 'non floating error'. 'non' means 'not a number'. Depending on your UDF this kind of error does not effectively happens at the first iteration. An example, if you are simulated a domain with a stagnant water as initial condition and you are calculated for the first iteration something like 1/Re therefore lets call it BOOM !!! because Re=0 . To find this kind of think there a simple way : reread your UDF.�<br />
<br />
'''MULTI PROCESSOR ISSUES''' -----"I've had similar problems recently with floating point errors on a multi processor simulation. The solution for my problem seems to be to run on a single processor, where it runs fine....?�<br />
<br />
'''WRONG INITIATION''' ----- Initiating the case with wrong conditions may lead to floating point error when the iterations start.<br />
<br />
<br />
==== What is the turbulent viscosity ratio warning and how can I handle? ====<br />
<br />
==== How do i carry out rotating body analysis, eg a rotating sphere or cylinder in flow? ====<br />
<br />
==== How do i get better and faster convergence? ====<br />
<br />
==== How to merge two mesh files and make one? ====<br />
To merge two mesh files the suggested utility is tmerge. The syntax of tmerge is simple.<br><br />
<i>utility tmerge -3d file1 file2 finalfile </i> <br><br />
To join the two interior faces use: <br><br />
<i>Grid->Fuse</i> <br><br />
from the menu with Fluent.<br />
<br />
==== What is the role of under-relaxation parameters? What should be the optimum choice of these parameters? ====<br />
They limit the influence of the previous iteration over the present one. If you choose small values it may prevent oscillations in residuum developing. At the same time the solution may need more time to converge. <br />
Keep the default values as they are given in FLUENT. You can decrease them gradually if necessary. Momentum 0.6, pressure 0.1, k 0.4, eps 0.4, mass source 1, viscosity 1.<br />
<br />
==== How can I determine the inputs for a porous media or porous jump from flow versus pressure drop data? ====<br />
<br />
==== How do I model heat conduction in a composite wall? ====<br />
<br />
==== What pressures should be specified at inlets and outlets for buoyancy flow problems? ====<br />
<br />
==== Are there any general guidelines on selecting a turbulence model? ====<br />
<br />
==== How can both turbulent and laminar flow be included in one model? ====<br />
<br />
==== How to start a 3D simulation with an compressible medium and temperature changes? What is important to consider ====<br />
<br />
==== How to run multiple cases in batch mode ==== <br />
This could be achieved by running it from journal file. The example journal file that runs two cases is given as <br><br />
<i><br />
file read-case-data xxx1.cas <br><br />
solve dual-time-iterate yyy1 <br><br />
file write-case-data zzz1.cas <br><br />
file read-case-data xxx2.cas <br><br />
yes <b>(comment: for discard cas dialog) </b><br><br />
solve dual-time-iterate yyy2 <br><br />
file write-case-data zzz2.cas <br></i><br />
<br />
<br />
<br />
<br />
==== What does the abbreviation mean?====<br />
<br />
CFD = Computational Fluid dynamics<br />
FEM = Finite element model<br />
UDF = User defined function<br />
<br />
=== FloWizard ===<br />
<br />
=== FIDAP ===<br />
<br />
=== POLYFLOW ===<br />
<br />
== Pre-processors ==<br />
<br />
=== Gambit ===<br />
<br />
=== Gambit Turbo ===<br />
<br />
=== TGrid ===<br />
<br />
== Application specific codes ==<br />
<br />
=== Icepak ===<br />
<br />
=== Airpak ===<br />
<br />
=== MixSim ===<br />
<br />
== Educational codes ==<br />
<br />
=== FlowLab ===<br />
<br />
<br />
[[Category: FAQ's]]<br />
<br />
{{stub}}</div>Zxaarhttp://www.cfd-online.com/Wiki/Fluent_FAQFluent FAQ2005-11-24T01:00:56Z<p>Zxaar: </p>
<hr />
<div>This section is empty. This is just a suggestion on how to structure it. Please feel free to add questions and answers here!<br />
<br />
== General purpose codes ==<br />
<br />
=== FLUENT ===<br />
<br />
<br />
==== What does the floating point error mean? How can I avoid it? ====<br />
<br />
The floating point error has been reported many times and discussed a lot. Here are some of the answers found in the Fluent Forum:<br />
<br />
'''SOLVER AND ITERATION''' -----I think if you set shorter time step, it may be good. Or changing little Under-Relaxiation-Factors, it may be good. In my experience, I set 1/3 Under-Relaxiation-Factors as default.� -----�also lower the values of under relaxation factor and use the coupled implicit solver� -----�Try to change under-relaxation factors and if it is unsteady problem maybe time step is to large.� -----�you can improve the ratio in the solve--control--limits, maybe that can help.� -----�you will need to decrease the Courant number� -----�If you still get the error, initialize the domain with nothing to 'Compute from...' Then click 'init'. Again select the surface from which you want to compute the initial values & iterate. This should work.� -----�Another reason could be a to high courant number - that means, that the steps between two iterations are too large and the change in the results is too large as well (high residuals)�<br />
<br />
'''GRID PROBLEMS''' -----�this error comes when I start scaling grid. in gambit, all my dimension is in mm, when in fluent i convert it in meter using buttone SCALE. after it, when i iterate, about hundred iteration, this error appeared. but when i not scale my drawing to m...and let it be as in gambit..then the iteration is success. -----�hi I think you should check your mesh grid mesh is very high. your problem solve by selection a low mesh.� -----�Your mesh is so heavy that your computers resources are not enough. try to use coarser mesh.�<br />
<br />
'''BOUNDARY CONDITIONS''' -----�In my case I had set a wall boundary condition instead of an axis boundary condition and then FLuent refuses to calculate telling me 'floating point error'.� -----�Your Boudary Conditions do not represent real physis.� -----�wrong boundary condition definition might cause the floating point error. For example setting an internal boundary as interior� -----�Once I had the problem, simulating a 2D chamber with a symmetry BC. I set the symmetry somewhere as �axe symmetric� and the floating point error occur� -----�check the turbulence parameter you set. reduce the turbulence intensity to less that one for first, say 50 iterations.<br />
<br />
'''USING A UDF''' -----�What I mean is really often when people creates UDF they generally forget that for the first iteration some variable can be zero. Therefore if you are divided a number by zero your solver will blow up telling you 'non floating error'. 'non' means 'not a number'. Depending on your UDF this kind of error does not effectively happens at the first iteration. An example, if you are simulated a domain with a stagnant water as initial condition and you are calculated for the first iteration something like 1/Re therefore lets call it BOOM !!! because Re=0 . To find this kind of think there a simple way : reread your UDF.�<br />
<br />
'''MULTI PROCESSOR ISSUES''' -----"I've had similar problems recently with floating point errors on a multi processor simulation. The solution for my problem seems to be to run on a single processor, where it runs fine....?�<br />
<br />
==== What is the turbulent viscosity ratio warning and how can I handle? ====<br />
<br />
==== How do i carry out rotating body analysis, eg a rotating sphere or cylinder in flow? ====<br />
<br />
==== How do i get better and faster convergence? ====<br />
<br />
==== How to merge two mesh files and make one? ====<br />
To merge two mesh files the suggested utility is tmerge. The syntax of tmerge is simple.<br><br />
<i>utility tmerge -3d file1 file2 finalfile </i> <br><br />
To join the two interior faces use: <br><br />
<i>Grid->Fuse</i> <br><br />
from the menu with Fluent.<br />
<br />
==== What is the role of under-relaxation parameters? What should be the optimum choice of these parameters? ====<br />
They limit the influence of the previous iteration over the present one. If you choose small values it may prevent oscillations in residuum developing. At the same time the solution may need more time to converge. <br />
Keep the default values as they are given in FLUENT. You can decrease them gradually if necessary. Momentum 0.6, pressure 0.1, k 0.4, eps 0.4, mass source 1, viscosity 1.<br />
<br />
==== How can I determine the inputs for a porous media or porous jump from flow versus pressure drop data? ====<br />
<br />
==== How do I model heat conduction in a composite wall? ====<br />
<br />
==== What pressures should be specified at inlets and outlets for buoyancy flow problems? ====<br />
<br />
==== Are there any general guidelines on selecting a turbulence model? ====<br />
<br />
==== How can both turbulent and laminar flow be included in one model? ====<br />
<br />
==== How to start a 3D simulation with an compressible medium and temperature changes? What is important to consider ====<br />
<br />
==== How to run multiple cases in batch mode ==== <br />
This could be achieved by running it from journal file. The example journal file that runs two cases is given as <br><br />
<i><br />
file read-case-data xxx1.cas <br><br />
solve dual-time-iterate yyy1 <br><br />
file write-case-data zzz1.cas <br><br />
file read-case-data xxx2.cas <br><br />
yes <b>(comment: for discard cas dialog) </b><br><br />
solve dual-time-iterate yyy2 <br><br />
file write-case-data zzz2.cas <br></i><br />
<br />
<br />
<br />
<br />
==== What does the abbreviation mean?====<br />
<br />
CFD = Computational Fluid dynamics<br />
FEM = Finite element model<br />
UDF = User defined function<br />
<br />
=== FloWizard ===<br />
<br />
=== FIDAP ===<br />
<br />
=== POLYFLOW ===<br />
<br />
== Pre-processors ==<br />
<br />
=== Gambit ===<br />
<br />
=== Gambit Turbo ===<br />
<br />
=== TGrid ===<br />
<br />
== Application specific codes ==<br />
<br />
=== Icepak ===<br />
<br />
=== Airpak ===<br />
<br />
=== MixSim ===<br />
<br />
== Educational codes ==<br />
<br />
=== FlowLab ===<br />
<br />
<br />
[[Category: FAQ's]]<br />
<br />
{{stub}}</div>Zxaarhttp://www.cfd-online.com/Wiki/Fluent_FAQFluent FAQ2005-11-22T04:57:34Z<p>Zxaar: </p>
<hr />
<div>This section is empty. This is just a suggestion on how to structure it. Please feel free to add questions and answers here!<br />
<br />
== General purpose codes ==<br />
<br />
=== FLUENT ===<br />
<br />
<br />
==== What does the floating point error mean? How can I avoid it? ====<br />
<br />
The floating point error has been reported many times and discussed a lot. Here are some of the answers found in the Fluent Forum:<br />
<br />
'''SOLVER AND ITERATION''' -----I think if you set shorter time step, it may be good. Or changing little Under-Relaxiation-Factors, it may be good. In my experience, I set 1/3 Under-Relaxiation-Factors as default.� -----�also lower the values of under relaxation factor and use the coupled implicit solver� -----�Try to change under-relaxation factors and if it is unsteady problem maybe time step is to large.� -----�you can improve the ratio in the solve--control--limits, maybe that can help.� -----�you will need to decrease the Courant number� -----�If you still get the error, initialize the domain with nothing to 'Compute from...' Then click 'init'. Again select the surface from which you want to compute the initial values & iterate. This should work.� -----�Another reason could be a to high courant number - that means, that the steps between two iterations are too large and the change in the results is too large as well (high residuals)�<br />
<br />
'''GRID PROBLEMS''' -----�this error comes when I start scaling grid. in gambit, all my dimension is in mm, when in fluent i convert it in meter using buttone SCALE. after it, when i iterate, about hundred iteration, this error appeared. but when i not scale my drawing to m...and let it be as in gambit..then the iteration is success. -----�hi I think you should check your mesh grid mesh is very high. your problem solve by selection a low mesh.� -----�Your mesh is so heavy that your computers resources are not enough. try to use coarser mesh.�<br />
<br />
'''BOUNDARY CONDITIONS''' -----�In my case I had set a wall boundary condition instead of an axis boundary condition and then FLuent refuses to calculate telling me 'floating point error'.� -----�Your Boudary Conditions do not represent real physis.� -----�wrong boundary condition definition might cause the floating point error. For example setting an internal boundary as interior� -----�Once I had the problem, simulating a 2D chamber with a symmetry BC. I set the symmetry somewhere as �axe symmetric� and the floating point error occur� -----�check the turbulence parameter you set. reduce the turbulence intensity to less that one for first, say 50 iterations.<br />
<br />
'''USING A UDF''' -----�What I mean is really often when people creates UDF they generally forget that for the first iteration some variable can be zero. Therefore if you are divided a number by zero your solver will blow up telling you 'non floating error'. 'non' means 'not a number'. Depending on your UDF this kind of error does not effectively happens at the first iteration. An example, if you are simulated a domain with a stagnant water as initial condition and you are calculated for the first iteration something like 1/Re therefore lets call it BOOM !!! because Re=0 . To find this kind of think there a simple way : reread your UDF.�<br />
<br />
'''MULTI PROCESSOR ISSUES''' -----"I've had similar problems recently with floating point errors on a multi processor simulation. The solution for my problem seems to be to run on a single processor, where it runs fine....?�<br />
<br />
==== What is the turbulent viscosity ratio warning and how can I handle? ====<br />
<br />
==== How do i carry out rotating body analysis, eg a rotating sphere or cylinder in flow? ====<br />
<br />
==== How do i get better and faster convergence? ====<br />
<br />
==== How to merge two mesh files and make one? ====<br />
To merge two mesh files the suggested utility is tmerge. The syntax of tmerge is simple.<br><br />
<i>utility tmerge -3d file1 file2 finalfile </i> <br><br />
To join the two interior faces use: <br><br />
<i>Grid->Fuse</i> <br><br />
from the menu with Fluent.<br />
<br />
==== What is the role of under-relaxation parameters? What should be the optimum choice of these parameters? ====<br />
They limit the influence of the previous iteration over the present one. If you choose small values it may prevent oscillations in residuum developing. At the same time the solution may need more time to converge. <br />
Keep the default values as they are given in FLUENT. You can decrease them gradually if necessary. Momentum 0.6, pressure 0.1, k 0.4, eps 0.4, mass source 1, viscosity 1.<br />
<br />
==== How can I determine the inputs for a porous media or porous jump from flow versus pressure drop data? ====<br />
<br />
==== How do I model heat conduction in a composite wall? ====<br />
<br />
==== What pressures should be specified at inlets and outlets for buoyancy flow problems? ====<br />
<br />
==== Are there any general guidelines on selecting a turbulence model? ====<br />
<br />
==== How can both turbulent and laminar flow be included in one model? ====<br />
<br />
==== How to start a 3D simulation with an compressible medium and temperature changes? What is important to consider ====<br />
<br />
==== What does the abbreviation mean?====<br />
<br />
CFD = Computational Fluid dynamics<br />
FEM = Finite element model<br />
UDF = User defined function<br />
<br />
=== FloWizard ===<br />
<br />
=== FIDAP ===<br />
<br />
=== POLYFLOW ===<br />
<br />
== Pre-processors ==<br />
<br />
=== Gambit ===<br />
<br />
=== Gambit Turbo ===<br />
<br />
=== TGrid ===<br />
<br />
== Application specific codes ==<br />
<br />
=== Icepak ===<br />
<br />
=== Airpak ===<br />
<br />
=== MixSim ===<br />
<br />
== Educational codes ==<br />
<br />
=== FlowLab ===<br />
<br />
<br />
[[Category: FAQ's]]<br />
<br />
{{stub}}</div>Zxaarhttp://www.cfd-online.com/Wiki/Runge_Kutta_methodsRunge Kutta methods2005-11-15T00:56:23Z<p>Zxaar: </p>
<hr />
<div>= Forth order Runge-Kutta Method =<br />
<br />
The fourth order Runge-Kutta method could be summarized as:<br />
<br />
==Algorithm==<br />
::<math>\dot y = f\left( {x,y} \right) </math><br />
::<math>k_1 = hf\left( {x_n ,y_n } \right) </math><br />
::<math>k_2 = hf\left( {x_n + {h \over 2},y_n + {{k_1 } \over 2}} \right) </math><br />
::<math>k_3 = hf\left( {x_n + {h \over 2},y_n + {{k_2 } \over 2}} \right) </math><br />
::<math>k_4 = hf\left( {x_n + h,y_n + k_3 } \right) </math><br />
::<math>y_{n + 1} = y_n + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6} </math><br />
<br />
<br />
<br />
{{stub}} <br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Euler_methodEuler method2005-11-15T00:55:57Z<p>Zxaar: </p>
<hr />
<div>== Euler Methods ==<br />
<br />
=== Explicit or Forward Euler ===<br />
:<math> \dot \phi = f\left( {t,\phi } \right)</math><br />
:<math>\phi ^{n + 1} = \phi ^n + f\left( {t_n ,\phi ^n } \right) </math><br />
<br />
=== Implicit or Backward Euler ===<br />
:<math> \dot \phi = f\left( {t,\phi } \right)</math><br />
:<math>\phi ^{n + 1} = \phi ^n + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right) </math><br />
<br />
{{stub}} <br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Euler_methodEuler method2005-11-14T04:13:47Z<p>Zxaar: </p>
<hr />
<div>== Euler Methods ==<br />
<br />
=== Explicit or Forward Euler ===<br />
:<math> \dot \phi = f\left( {t,\phi } \right)</math><br />
:<math>\phi ^{n + 1} = \phi ^n + f\left( {t_n ,\phi ^n } \right) </math><br />
<br />
=== Implicit or Backward Euler ===<br />
:<math> \dot \phi = f\left( {t,\phi } \right)</math><br />
:<math>\phi ^{n + 1} = \phi ^n + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right) </math><br />
<br />
<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Euler_methodEuler method2005-11-14T04:13:05Z<p>Zxaar: </p>
<hr />
<div>== Euler Methods ==<br />
<br />
=== Explicit or Forward Euler ===<br />
:<math> \dot \phi = f\left( {t,\phi } \right)</math><br />
:<math>\phi ^{n + 1} = \phi ^n + f\left( {t_n ,\phi ^n } \right) </math><br />
<br />
=== Implicit or Backward Euler ===<br />
:<math> \dot \phi = f\left( {t,\phi } \right)</math><br />
:<math>\phi ^{n + 1} = \phi ^n + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right) </math></div>Zxaarhttp://www.cfd-online.com/Wiki/Runge_Kutta_methodsRunge Kutta methods2005-11-14T04:04:50Z<p>Zxaar: </p>
<hr />
<div>= Forth order Runge-Kutta Method =<br />
<br />
The fourth order Runge-Kutta method could be summarized as:<br />
<br />
==Algorithm==<br />
::<math>\dot y = f\left( {x,y} \right) </math><br />
::<math>k_1 = hf\left( {x_n ,y_n } \right) </math><br />
::<math>k_2 = hf\left( {x_n + {h \over 2},y_n + {{k_1 } \over 2}} \right) </math><br />
::<math>k_3 = hf\left( {x_n + {h \over 2},y_n + {{k_2 } \over 2}} \right) </math><br />
::<math>k_4 = hf\left( {x_n + h,y_n + k_3 } \right) </math><br />
::<math>y_{n + 1} = y_n + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6} </math><br />
<br />
<br />
<br />
<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Implicit_second_order_methodImplicit second order method2005-11-01T00:55:55Z<p>Zxaar: </p>
<hr />
<div>= Implicit Second Order Method =<br />
<br />
The implicit second order method involves the derivatives of the next time level. Due to this reason they are iterative in nature. The second order time integration scheme is given by: <br><br />
<br />
==Algorithm==<br />
<br />
: for r:= 1 step 1 until M do <br><br />
::<math>\phi ^{n + 1} = {4 \over 3}\phi ^n - {1 \over 3}\phi ^{n - 1} + {2 \over 3}\dot \phi \left( {t_{n + 1} ,\phi ^{n + 1} } \right) \bullet \Delta t<br />
</math><br />
: end (r-loop) <br> <br />
<br />
<i> Where M is maximum number of internal iterations. </i><br />
<br />
<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Runge_Kutta_methodsRunge Kutta methods2005-11-01T00:49:34Z<p>Zxaar: </p>
<hr />
<div>= Forth order Runge-Kutta Method =<br />
<br />
The forth order Runge-Kutta method could be summarized as:<br />
<br />
==Algorithm==<br />
::<math>\dot y = f\left( {x,y} \right) </math><br />
::<math>k_1 = hf\left( {x_n ,y_n } \right) </math><br />
::<math>k_2 = hf\left( {x_n + {h \over 2},y_n + {{k_1 } \over 2}} \right) </math><br />
::<math>k_3 = hf\left( {x_n + {h \over 2},y_n + {{k_2 } \over 2}} \right) </math><br />
::<math>k_4 = hf\left( {x_n + h,y_n + k_3 } \right) </math><br />
::<math>y_{n + 1} = y_n + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6} </math><br />
<br />
<br />
<br />
<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Runge_Kutta_methodsRunge Kutta methods2005-11-01T00:49:06Z<p>Zxaar: </p>
<hr />
<div><br />
= Forth order Runge-Kutta Method =<br />
<br />
The forth order Runge-Kutta method could be summarized as:<br />
<br />
==Algorithm==<br />
::<math>\dot y = f\left( {x,y} \right) </math><br />
::<math>k_1 = hf\left( {x_n ,y_n } \right) </math><br />
::<math>k_2 = hf\left( {x_n + {h \over 2},y_n + {{k_1 } \over 2}} \right) </math><br />
::<math>k_3 = hf\left( {x_n + {h \over 2},y_n + {{k_2 } \over 2}} \right) </math><br />
::<math>k_4 = hf\left( {x_n + h,y_n + k_3 } \right) </math><br />
::<math>y_{n + 1} = y_n + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6} </math></div>Zxaarhttp://www.cfd-online.com/Wiki/Rhie-Chow_interpolationRhie-Chow interpolation2005-10-24T05:51:52Z<p>Zxaar: </p>
<hr />
<div>we have at each cell descretised equation in this form, <br><br />
:<math> a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V} </math> ; <br><br />
For continuity we have <br><br />
:<math> \sum\limits_{faces} \left[ {\frac{1}{{a_p }}H} \right]_{face} = \sum\limits_{faces} \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face} </math> <br><br />
<br />
where <br><br />
:<math> H = \sum\limits_{neighbours} {a_l } \vec v_l </math> <br><br />
<br />
This interpolation of variables H and <math> {\nabla p} </math> based on coefficients <math> a_p </math> for [[Velocity-pressure coupling | pressure velocity coupling ]] is called <b>Rhie-Chow interpolation</b>.<br />
<br />
----<br />
<i> Return to: <br><br />
# [[Numerical methods | Numerical Methods]]<br />
# [[Solution of Navier-Stokes equation]]<br />
</i></div>Zxaarhttp://www.cfd-online.com/Wiki/Velocity-pressure_couplingVelocity-pressure coupling2005-10-24T05:50:33Z<p>Zxaar: </p>
<hr />
<div>If we consider the discretised form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter-equation coupling is called velocity pressure coupling. A special treatment is required in order to velocity-pressure coupling. The methods such as: <br><br />
# SIMPLE<br />
# SIMPLER<br />
# SIMPLEC<br />
# PISO <br />
provide an useful means of doing this for segregated solvers. However it is possible to solve the system of Navier-Stokes equations in coupled manner, taking care of inter equation coupling in a single matrix. <br />
<br />
==Formulation==<br />
we have at each cell descretised equation in this form, <br><br />
:<math> a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V} </math> ; Where V = Volume of cell.<br><br />
According to [[Rhie-Chow interpolation]], we have <br><br />
:<math> \vec v_P = \frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }} - \frac{{\nabla p}}{{a_p V}} </math> <br><br />
<br />
For continuity : <br><br />
:<math> \sum\limits_{faces} {\vec v_f \bullet \vec A} = 0 </math> <br><br />
so we get: <br><br />
:<math> \sum\limits_{faces} \left[ {\frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }}} \right]_{face} - \sum\limits_{faces} \left[ {\frac{{\nabla p}}{{a_p V}}} \right]_{face} = 0 </math> <br><br />
this gives us: <br><br />
:<math> \sum\limits_{faces} \left[ {\frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }}} \right]_{face} = \sum\limits_{faces} \left[ {\frac{{\nabla p}}{{a_p V}}} \right]_{face} </math><br><br />
defining <math> H = \sum\limits_{neighbours} {a_l } \vec v_l </math> <br><br />
:<math> \sum\limits_{faces} \left[ {\frac{1}{{a_p }}H} \right]_{face} = \sum\limits_{faces} \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face} </math> <br><br />
from this a pressure correction equation could be formed as: <br><br />
:<math> \sum\limits_{faces} \left[ {\frac{1}{{a_p }}H} \right]_{face} - \sum\limits_{faces} \left[ {\frac{1}{{a_p }}\frac{{\nabla p^* }}{V}} \right]_{face} = \sum\limits_{faces} \left[ {\frac{1}{{a_p }}\frac{{\nabla p^' }}{V}} \right]_{face} </math> <br><br />
This is a poisson equation. <br />
<br />
Here the gradients could be used from previous iteration.<br />
<br />
<br />
==SIMPLE==<br />
See [[SIMPLE algorithm]]<br />
== SIMPLER==<br />
See [[SIMPLER algorithm]]<br />
<br />
== SIMPLEC==<br />
See [[SIMPLEC algorithm]]<br />
<br />
== PISO ==<br />
See [[PISO algorithm]]<br />
<br />
<br />
----<br />
<i> Return to: <br><br />
# [[Numerical methods | Numerical Methods]]<br />
# [[Solution of Navier-Stokes equation]]<br />
</i></div>Zxaarhttp://www.cfd-online.com/Wiki/Velocity-pressure_couplingVelocity-pressure coupling2005-10-24T00:07:54Z<p>Zxaar: </p>
<hr />
<div>If we consider the discretised form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter-equation coupling is called velocity pressure coupling. A special treatment is required in order to velocity-pressure coupling. The methods such as: <br><br />
# SIMPLE<br />
# SIMPLER<br />
# SIMPLEC<br />
# PISO <br />
provide an useful means of doing this for segregated solvers. However it is possible to solve the system of Navier-Stokes equations in coupled manner, taking care of inter equation coupling in a single matrix. <br />
<br />
==Formulation==<br />
we have at each cell descretised equation in this form, <br><br />
:<math> a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V} </math> ; <br><br />
According to [[Rhie-Chow interpolation]], we have <br><br />
:<math> \vec v_P = \frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }} - \frac{{\nabla p}}{{a_p V}} </math> <br><br />
<br />
For continuity : <br><br />
:<math> \sum\limits_{faces} {\vec v_f \bullet \vec A} = 0 </math> <br><br />
so we get: <br><br />
:<math>\left[ {\frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }}} \right]_{face} - \left[ {\frac{{\nabla p}}{{a_p V}}} \right]_{face} = 0 </math> <br><br />
this gives us: <br><br />
:<math> \left[ {\frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }}} \right]_{face} = \left[ {\frac{{\nabla p}}{{a_p V}}} \right]_{face} </math><br><br />
defining <math> H = \sum\limits_{neighbours} {a_l } \vec v_l </math> <br><br />
:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face} </math> <br><br />
from this a pressure correction equation could be formed as: <br><br />
:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face} - \left[ {\frac{1}{{a_p }}\frac{{\nabla p^* }}{V}} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p^' }}{V}} \right]_{face} </math> <br><br />
This is a poisson equation.<br />
<br />
Here the gradients could be used from previous iteration.<br />
<br />
<br />
==SIMPLE==<br />
See [[SIMPLE algorithm]]<br />
== SIMPLER==<br />
See [[SIMPLER algorithm]]<br />
<br />
== SIMPLEC==<br />
See [[SIMPLEC algorithm]]<br />
<br />
== PISO ==<br />
See [[PISO algorithm]]<br />
<br />
<br />
----<br />
<i> Return to: <br><br />
# [[Numerical methods | Numerical Methods]]<br />
# [[Solution of Navier-Stokes equation]]<br />
</i></div>Zxaarhttp://www.cfd-online.com/Wiki/Rhie-Chow_interpolationRhie-Chow interpolation2005-10-24T00:06:04Z<p>Zxaar: </p>
<hr />
<div>we have at each cell descretised equation in this form, <br><br />
:<math> a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V} </math> ; <br><br />
:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face} </math> <br><br />
<br />
where <br><br />
:<math> H = \sum\limits_{neighbours} {a_l } \vec v_l </math> <br><br />
<br />
This interpolation of variables H and <math> {\nabla p} </math> based on coefficients <math> a_p </math> for [[Velocity-pressure coupling | pressure velocity coupling ]] is called <b>Rhie-Chow interpolation</b>.<br />
<br />
----<br />
<i> Return to: <br><br />
# [[Numerical methods | Numerical Methods]]<br />
# [[Solution of Navier-Stokes equation]]<br />
</i></div>Zxaarhttp://www.cfd-online.com/Wiki/Rhie-Chow_interpolationRhie-Chow interpolation2005-10-23T11:39:15Z<p>Zxaar: </p>
<hr />
<div>we have at each cell descretised equation in this form, <br><br />
:<math> a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V} </math> ; <br><br />
:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face} </math> <br><br />
<br />
where <br><br />
:<math> H = \sum\limits_{neighbours} {a_l } \vec v_l </math> <br><br />
<br />
This interpolation of variables H and <math> {\nabla p} </math> based on coefficients <math> a_p </math> for pressure velocity coupling is called <b>Rhie-Chow interpolation</b>.<br />
<br />
----<br />
<i> Return to: <br><br />
# [[Numerical methods | Numerical Methods]]<br />
# [[Solution of Navier-Stokes equation]]<br />
</i></div>Zxaarhttp://www.cfd-online.com/Wiki/Rhie-Chow_interpolationRhie-Chow interpolation2005-10-23T11:34:52Z<p>Zxaar: </p>
<hr />
<div>we have at each cell descretised equation in this form, <br><br />
:<math> a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V} </math> ; <br><br />
:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face} </math> <br><br />
<br />
where <math> H = \sum\limits_{neighbours} {a_l } \vec v_l </math> <br><br />
<br />
<br />
<br />
----<br />
<i> Return to: <br><br />
# [[Numerical methods | Numerical Methods]]<br />
# [[Solution of Navier-Stokes equation]]<br />
</i></div>Zxaarhttp://www.cfd-online.com/Wiki/Velocity-pressure_couplingVelocity-pressure coupling2005-10-23T11:31:48Z<p>Zxaar: </p>
<hr />
<div>If we consider the discretised form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter-equation coupling is called velocity pressure coupling. A special treatment is required in order to velocity-pressure coupling. The methods such as: <br><br />
# SIMPLE<br />
# SIMPLER<br />
# SIMPLEC<br />
# PISO <br />
provide an useful means of doing this for segregated solvers. However it is possible to solve the system of Navier-Stokes equations in coupled manner, taking care of inter equation coupling in a single matrix. <br />
<br />
==Formulation==<br />
we have at each cell descretised equation in this form, <br><br />
:<math> a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V} </math> ; <br><br />
we have <br><br />
:<math> \vec v_P = \frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }} - \frac{{\nabla p}}{{a_p V}} </math> <br><br />
<br />
For continuity : <br><br />
:<math> \sum\limits_{faces} {\vec v_f \bullet \vec A} = 0 </math> <br><br />
so we get: <br><br />
:<math>\left[ {\frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }}} \right]_{face} - \left[ {\frac{{\nabla p}}{{a_p V}}} \right]_{face} = 0 </math> <br><br />
this gives us: <br><br />
:<math> \left[ {\frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }}} \right]_{face} = \left[ {\frac{{\nabla p}}{{a_p V}}} \right]_{face} </math><br><br />
defining <math> H = \sum\limits_{neighbours} {a_l } \vec v_l </math> <br><br />
:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face} </math> <br><br />
from this a pressure correction equation could be formed as: <br><br />
:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face} - \left[ {\frac{1}{{a_p }}\frac{{\nabla p^* }}{V}} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p^' }}{V}} \right]_{face} </math> <br><br />
This is a poisson equation.<br />
<br />
Here the gradients could be used from previous iteration.<br />
<br />
<br />
==SIMPLE==<br />
See [[SIMPLE algorithm]]<br />
== SIMPLER==<br />
See [[SIMPLER algorithm]]<br />
<br />
== SIMPLEC==<br />
See [[SIMPLEC algorithm]]<br />
<br />
== PISO ==<br />
See [[PISO algorithm]]<br />
<br />
<br />
----<br />
<i> Return to: <br><br />
# [[Numerical methods | Numerical Methods]]<br />
# [[Solution of Navier-Stokes equation]]<br />
</i></div>Zxaarhttp://www.cfd-online.com/Wiki/Rhie-Chow_interpolationRhie-Chow interpolation2005-10-23T11:28:14Z<p>Zxaar: </p>
<hr />
<div>we have at each cell descretised equation in this form, <br><br />
:<math> a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V} </math> ; <br><br />
we have <br><br />
:<math> \vec v_P = \frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }} - \frac{{\nabla p}}{{a_p V}} </math> <br><br />
<br />
For continuity : <br><br />
:<math> \sum\limits_{faces} {\vec v_f \bullet \vec A} = 0 </math> <br><br />
so we get: <br><br />
:<math>\left[ {\frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }}} \right]_{face} - \left[ {\frac{{\nabla p}}{{a_p V}}} \right]_{face} = 0 </math> <br><br />
this gives us: <br><br />
:<math> \left[ {\frac{{\sum\limits_{neighbours} {a_l } \vec v_l }}{{a_p }}} \right]_{face} = \left[ {\frac{{\nabla p}}{{a_p V}}} \right]_{face} </math><br><br />
defining <math> H = \sum\limits_{neighbours} {a_l } \vec v_l </math> <br><br />
:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face} </math> <br><br />
from this a pressure correction equation could be formed as: <br><br />
:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face} - \left[ {\frac{1}{{a_p }}\frac{{\nabla p^* }}{V}} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p^' }}{V}} \right]_{face} </math> <br><br />
This is a poisson equation.<br />
<br />
Here the gradients could be used from previous iteration.</div>Zxaarhttp://www.cfd-online.com/Wiki/SIMPLE_algorithmSIMPLE algorithm2005-10-23T10:27:54Z<p>Zxaar: </p>
<hr />
<div>==SIMPLE==<br />
<br />
If a steady-state problem is being solved iteratively, it is not necessary to fully resolve<br />
the linear pressure-velocity coupling, as the changes between consecutive solutions<br />
are no longer small. <br />
The SIMPLE algorithm:<br />
<br />
* An approximation of the velocity field is obtained by solving the momentum equation. The pressure gradient term is calculated using the pressure distribution from the previous iteration or an initial guess.<br />
* The pressure equation is formulated and solved in order to obtain the new pressure distribution.<br />
* Velocities are corrected and a new set of conservative fluxes is calculated.<br />
<br />
<br />
==SIMPLE Solver Algorithm ==<br />
The algorithm may be summarized as follows: <br />
<br />
The basic steps in the solution update are as follows: <br />
<br />
#Set the boundary conditions.<br />
#Computed the gradients of velocity and pressure.<br />
#Solve the discretized momentum equation to compute the intermediate velocity field . <br />
#Compute the uncorrected mass fluxes at faces . <br />
#Solve the pressure correction equation to produce cell values of the pressure correction .<br />
#Update the pressure field: <math> p^{k + 1} = p^k + urf \bullet p^' </math> where urf is the under-relaxation factor for pressure.<br />
#Update the boundary pressure corrections <math> p_b^' </math>.<br />
#Correct the face mass fluxes: <math>\dot m_f^{k + 1} = \dot m_f^* + \dot m_f^' </math><br />
#Correct the cell velocities: <math> \vec v^{k + 1} = \vec v^* - \frac{{Vol\nabla p^' }}{{\vec a_P^v }} </math> ; where <math> {\nabla p^' } </math> is the gradient of the pressure corrections, <math> {\vec a_P^v } </math> is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume.<br />
#Update density due to pressure changes.<br />
<br />
<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Numerical_methodsNumerical methods2005-10-14T00:58:33Z<p>Zxaar: </p>
<hr />
<div>== Numerical Aspects of CFD ==<br />
This section covers the numerical soul of CFD. <br />
# [[Introduction to numerical methods]]<br />
# Geometrical Calculations<br />
## [[Area calculations]]<br />
## [[Volume calculations]]<br />
# Gradient calculations<br />
## [[Finite volume method of gradient calculation]]<br />
# Discretisation<br />
## [[Finite differences]]<br />
## [[Finite volume]]<br />
### [[Discretisation of convective term]]<br />
### [[Discretisation of diffusive term]]<br />
## [[Finite element]]<br />
## [[Time discretisation]]<br />
### [[Euler method]]<br />
### [[Predictor corrector methods]]<br />
#### [[Runge Kutta methods]]<br />
#### [[Adams Bashforth method]]<br />
#### [[Adams Moulton method]]<br />
### [[Implicit second order method]]<br />
# Linear equation systems<br />
## [[Introduction and need]]<br />
## Matrix Related<br />
### [[Matrix factorisation]]<br />
#### [[LU factorisation for sparse matrices]]<br />
#### [[Incomplete Cholesky factorization]]<br />
## Direct numerical solutions<br />
### [[Gauss elimination]]<br />
### [[LU decomposition method]]<br />
### Direct solution to tridiagonal matrix<br />
#### [[Thomas algorithm]]<br />
## Iterative solutions<br />
### [[Basic concept of iterative solutions]]<br />
### [[Gauss-Seidel method]]<br />
### [[Jacobi method]]<br />
### [[Successive over-relaxation method]]<br />
### [[Stone's method]]<br />
### [[Alternating direction implicit (ADI) method]]<br />
### [[Congugate gradient methods]]<br />
#### [[Conjugate gradient method of Golub and van Loan]]<br />
#### [[Biconjugate gradient method]]<br />
#### [[Biconjugate gradient stabilized method]]<br />
## [[Multigrid methods]]<br />
### [[Geometric multigrid]]<br />
### [[Additive corrective multigrid]]<br />
# [[Solution of Poisson's equation]]<br />
# [[Solution of Navier-Stokes equation]]<br />
## [[Velocity-pressure coupling]]<br />
### [[Rhie-Chow interpolation]]<br />
## [[Fully coupled methods - FC]]<br />
## [[DeCoupled methods - DC]]<br />
### [[SIMPLE algorithm]]<br />
### [[SIMPLEC algorithm - SIMPLE Consistent]]<br />
### [[SIMPLEM algorithm - SIMPLE-Modified]]<br />
### [[SIMPLEX algorithm]]<br />
### [[SIMPLEST algorithm - SIMPLE ShorTened]]<br />
### [[SIMPLER algorithm - SIMPLE - Revised]]<br />
### [[PISO algorithm - Pressure Implicit with Split Operator]]<br />
### [[PRIME algorithm - PRessure Implicit Momentum Explicit]]<br />
### [[MSIMPLEC, MPISO , SIMPLESSEC , SIMPLESSE]]<br />
### [[CPC - Compressible Pressure Correction algorithm]]<br />
### [[MCBA - Mass Conservation Based Algorithms]]<br />
### [[GCBA - Geometric Conservation Based Algorithms]]<br />
### [[IPSA - Inter-Phase Slip Algorithm]] <br />
### [[CPI - Consistent Physical Interpolation]]<br />
### [[MWIM - Momentum Weighted Interpolation Method]]<br />
### [[PWIM - Pressure Weighted Interpolation Method]]<br />
### [[ACM - Artificial Compressibility Method]]<br />
# [[Solution of Euler equation]]<br />
# [[Efficiency and stability]]<br />
## Limiters<br />
### [[Flux limiters]]<br />
### [[Gradient limiters]]<br />
# [[Meshless methods]]<br />
# [[Overset grids]]<br />
# [[Panel method]]<br />
# CFD Related algorithms<br />
## Wall distance Calculations<br />
### [[Moore's kd-tree algorithm]]<br />
### [[Transport equation based wall distance calculation]]</div>Zxaarhttp://www.cfd-online.com/Wiki/Numerical_methodsNumerical methods2005-10-14T00:53:19Z<p>Zxaar: </p>
<hr />
<div>== Numerical Aspects of CFD ==<br />
This section covers the numerical soul of CFD. <br />
# [[Introduction to numerical methods]]<br />
# Geometrical Calculations<br />
## [[Area calculations]]<br />
## [[Volume calculations]]<br />
# Gradient calculations<br />
## [[Finite volume method of gradient calculation]]<br />
# Discretisation<br />
## [[Finite differences]]<br />
## [[Finite volume]]<br />
### [[Discretisation of convective term]]<br />
### [[Discretisation of diffusive term]]<br />
## [[Finite element]]<br />
## [[Time discretisation]]<br />
# Linear equation systems<br />
## [[Introduction and need]]<br />
## Matrix Related<br />
### [[Matrix factorisation]]<br />
#### [[LU factorisation for sparse matrices]]<br />
#### [[Incomplete Cholesky factorization]]<br />
## Direct numerical solutions<br />
### [[Gauss elimination]]<br />
### [[LU decomposition method]]<br />
### Direct solution to tridiagonal matrix<br />
#### [[Thomas algorithm]]<br />
## Iterative solutions<br />
### [[Basic concept of iterative solutions]]<br />
### [[Gauss-Seidel method]]<br />
### [[Jacobi method]]<br />
### [[Successive over-relaxation method]]<br />
### [[Stone's method]]<br />
### [[Alternating direction implicit (ADI) method]]<br />
### [[Congugate gradient methods]]<br />
#### [[Conjugate gradient method of Golub and van Loan]]<br />
#### [[Biconjugate gradient method]]<br />
#### [[Biconjugate gradient stabilized method]]<br />
## [[Multigrid methods]]<br />
### [[Geometric multigrid]]<br />
### [[Additive corrective multigrid]]<br />
# [[Solution of Poisson's equation]]<br />
# [[Solution of Navier-Stokes equation]]<br />
## [[Velocity-pressure coupling]]<br />
### [[Rhie-Chow interpolation]]<br />
## [[Fully coupled methods - FC]]<br />
## [[DeCoupled methods - DC]]<br />
### [[SIMPLE algorithm]]<br />
### [[SIMPLEC algorithm - SIMPLE Consistent]]<br />
### [[SIMPLEM algorithm - SIMPLE-Modified]]<br />
### [[SIMPLEX algorithm]]<br />
### [[SIMPLEST algorithm - SIMPLE ShorTened]]<br />
### [[SIMPLER algorithm - SIMPLE - Revised]]<br />
### [[PISO algorithm - Pressure Implicit with Split Operator]]<br />
### [[PRIME algorithm - PRessure Implicit Momentum Explicit]]<br />
### [[MSIMPLEC, MPISO , SIMPLESSEC , SIMPLESSE]]<br />
### [[CPC - Compressible Pressure Correction algorithm]]<br />
### [[MCBA - Mass Conservation Based Algorithms]]<br />
### [[GCBA - Geometric Conservation Based Algorithms]]<br />
### [[IPSA - Inter-Phase Slip Algorithm]] <br />
### [[CPI - Consistent Physical Interpolation]]<br />
### [[MWIM - Momentum Weighted Interpolation Method]]<br />
### [[PWIM - Pressure Weighted Interpolation Method]]<br />
### [[ACM - Artificial Compressibility Method]]<br />
# [[Solution of Euler equation]]<br />
# [[Efficiency and stability]]<br />
## Limiters<br />
### [[Flux limiters]]<br />
### [[Gradient limiters]]<br />
# [[Meshless methods]]<br />
# [[Overset grids]]<br />
# [[Panel method]]<br />
# CFD Related algorithms<br />
## Wall distance Calculations<br />
### [[Moore's kd-tree algorithm]]<br />
### [[Transport equation based wall distance calculation]]</div>Zxaarhttp://www.cfd-online.com/Wiki/Numerical_methodsNumerical methods2005-10-14T00:51:45Z<p>Zxaar: </p>
<hr />
<div>== Numerical Aspects of CFD ==<br />
This section covers the numerical soul of CFD. <br />
# [[Introduction to numerical methods]]<br />
# Geometrical Calculations<br />
## [[Area calculations]]<br />
## [[Volume calculations]]<br />
# Gradient calculations<br />
## [[Finite volume method of gradient calculation]]<br />
# Discretisation<br />
## [[Finite differences]]<br />
## [[Finite volume]]<br />
### [[Discretisation of convective term]]<br />
### [[Discretisation of diffusive term]]<br />
## [[Finite element]]<br />
## [[Time discretisation]]<br />
# Linear equation systems<br />
## [[Introduction and need]]<br />
## Matrix Related<br />
### [[Matrix factorisation]]<br />
#### [[LU factorisation for sparse matrices]]<br />
#### [[Incomplete Cholesky factorization]]<br />
## Direct numerical solutions<br />
### [[Gauss elimination]]<br />
### [[LU decomposition method]]<br />
### Direct solution to tridiagonal matrix<br />
#### [[Thomas algorithm]]<br />
## Iterative solutions<br />
### [[Basic concept of iterative solutions]]<br />
### [[Gauss-Seidel method]]<br />
### [[Jacobi method]]<br />
### [[Successive over-relaxation method]]<br />
### [[Stone's method]]<br />
### [[Alternating direction implicit (ADI) method]]<br />
### [[Congugate gradient methods]]<br />
#### [[Conjugate gradient method of Golub and van Loan]]<br />
#### [[Biconjugate gradient method]]<br />
#### [[Biconjugate gradient stabilized method]]<br />
## [[Multigrid methods]]<br />
### [[Geometric multigrid]]<br />
### [[Additive corrective multigrid]]<br />
# [[Solution of Poisson's equation]]<br />
# [[Solution of Navier-Stokes equation]]<br />
## [[Velocity-pressure coupling]]<br />
### [[Rhie-Chow interpolation]]<br />
## [[Fully coupled methods - FC]]<br />
## [[DeCoupled methods - DC]]<br />
### [[SIMPLE algorithm]]<br />
### [[SIMPLEC algorithm - SIMPLE Consistent]]<br />
### [[SIMPLEM algorithm - SIMPLE-Modified]]<br />
### [[SIMPLEX algorithm]]<br />
### [[SIMPLEST algorithm - SIMPLE ShorTened]]<br />
### [[SIMPLER algorithm - SIMPLE - Revised]]<br />
### [[PISO algorithm - Pressure Implicit with Split Operator]]<br />
### [[PRIME algorithm - PRessure Implicit Momentum Explicit]]<br />
### [[MSIMPLEC, MPISO , SIMPLESSEC , SIMPLESSE]]<br />
### [[CPC - Compressible Pressure Correction algorithm]]<br />
### [[MCBA - Mass Conservation Based Algorithms]]<br />
### [[GCBA - Geometric Conservation Based Algorithms]]<br />
### [[IPSA - Inter-Phase Slip Algorithm]] <br />
### [[CPI - Consistent Physical Interpolation]]<br />
### [[MWIM - Momentum Weighted Interpolation Method]]<br />
### [[PWIM - Pressure Weighted Interpolation Method]]<br />
### [[ACM - Artificial Compressibility Method]]<br />
# [[Efficiency and stability]]<br />
## Limiters<br />
### [[Flux limiters]]<br />
### [[Gradient limiters]]<br />
# [[Solution of Euler equation]]<br />
# [[Meshless methods]]<br />
# [[Overset grids]]<br />
# [[Panel method]]<br />
# CFD Related algorithms<br />
## Wall distance Calculations<br />
### [[Moore's kd-tree algorithm]]<br />
### [[Transport equation based wall distance calculation]]</div>Zxaarhttp://www.cfd-online.com/Wiki/Potential_flowPotential flow2005-10-04T05:17:05Z<p>Zxaar: </p>
<hr />
<div>A flow in which vorticity is zero is called potential flow, or irrotational flow. Since the vorticity is zero<br />
<br />
<math><br />
\omega = \nabla \times u = 0<br />
</math><br />
<br />
it implies that the velocity is the gradient of a scalar field called the velocity potential, and usually denoted as <math>\phi</math><br />
<br />
<math><br />
u_i = \frac{\partial \phi}{\partial x_i}<br />
</math><br />
<br />
At high Reynolds numbers, flow past slender bodies is attached (no boundary layer separation) and the boundary layers are thin. In such situations vorticity is confined to the thin boundary layers and the rest of the flow is irrotational.<br />
<br />
== Governing equations ==<br />
<br />
<br />
<br />
== External Links ==<br />
* [http://www.ecs.syr.edu/centers/simfluid/red/superpos.html Applet Simulating 2D Potential Flow]</div>Zxaarhttp://www.cfd-online.com/Wiki/Velocity-pressure_couplingVelocity-pressure coupling2005-10-04T00:10:23Z<p>Zxaar: </p>
<hr />
<div>If we consider the discretised form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter-equation coupling is called velocity pressure coupling. A special treatment is required in order to velocity-pressure coupling. The methods such as: <br><br />
# SIMPLE<br />
# SIMPLER<br />
# SIMPLEC<br />
# PISO <br />
provide an useful means of doing this for segregated solvers. However it is possible to solve the system of Navier-Stokes equations in coupled manner, taking care of inter equation coupling in a single matrix. <br />
<br />
<br />
<br />
==SIMPLE==<br />
See [[SIMPLE algorithm]]<br />
== SIMPLER==<br />
See [[SIMPLER algorithm]]<br />
<br />
== SIMPLEC==<br />
See [[SIMPLEC algorithm]]<br />
<br />
== PISO ==<br />
See [[PISO algorithm]]<br />
<br />
<br />
----<br />
<i> Return to: <br><br />
# [[Numerical methods | Numerical Methods]]<br />
# [[Solution of Navier-Stokes equation]]<br />
</i></div>Zxaarhttp://www.cfd-online.com/Wiki/Velocity-pressure_couplingVelocity-pressure coupling2005-10-04T00:04:24Z<p>Zxaar: </p>
<hr />
<div>If we consider the discretised form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter-equation coupling is called velocity pressure coupling. A special treatment is required in order to velocity-pressure coupling. The methods such as: <br><br />
# SIMPLE<br />
# SIMPLER<br />
# SIMPLEC<br />
# PISO <br />
provide an useful means of doing this for segregated solvers. However it is possible to solve the system of Navier-Stokes equations in coupled manner, taking care of inter equation coupling in a single matrix. <br />
<br />
<br />
<br />
==SIMPLE==<br />
See [[SIMPLE algorithm]]<br />
== SIMPLER==<br />
See [[SIMPLER algorithm]]<br />
<br />
== SIMPLEC==<br />
See [[SIMPLEC algorithm]]<br />
<br />
== PISO ==<br />
See [[PISO algorithm]]<br />
<br />
<br />
----<br />
<i> Return to <br><br />
# [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Velocity-pressure_couplingVelocity-pressure coupling2005-10-04T00:03:13Z<p>Zxaar: </p>
<hr />
<div>If we consider the discretised form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter-equation coupling is called velocity pressure coupling. A special treatment is required in order to velocity-pressure coupling. The methods such as: <br><br />
# SIMPLE<br />
# SIMPLER<br />
# SIMPLEC<br />
# PISO <br />
provide an useful means of doing this for segregated solvers. However it is possible to solve the system of Navier-Stokes equations in coupled manner, taking care of inter equation coupling in a single matrix. <br />
<br />
<br />
<br />
==SIMPLE==<br />
See [[SIMPLE algorithm]]<br />
== SIMPLER==<br />
See [[SIMPLER algorithm]]<br />
<br />
== SIMPLEC==<br />
See [[SIMPLEC algorithm]]<br />
<br />
== PISO ==<br />
See [[PISO algorithm]]<br />
<br />
<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Velocity-pressure_couplingVelocity-pressure coupling2005-10-03T11:27:00Z<p>Zxaar: </p>
<hr />
<div>If we consider the discretised form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter-equation coupling is called velocity pressure coupling. A special treatment is required in order to velocity-pressure coupling. The methods such as: <br><br />
# SIMPLE<br />
# SIMPLER<br />
# SIMPLEC<br />
# PISO <br />
provide an useful means of doing this for segregated solvers. However it is possible to solve the system of Navier-Stokes equations in coupled manner, taking care of inter equation coupling in a single matrix. <br />
<br />
<br />
<br />
==SIMPLE==<br />
<br />
== SIMPLER==<br />
<br />
== SIMPLEC==<br />
<br />
== PISO ==<br />
<br />
<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Geometric_multigrid_-_FASGeometric multigrid - FAS2005-10-03T08:38:46Z<p>Zxaar: </p>
<hr />
<div>==Geometric Multigrid or (FAS) ==<br />
In Geometric multigrid a hierarchy of meshes is generated.The discretized equations are evaluated on every level. The advantage of geometric multigrid over algebraic multigrid is that the former should perform better for non-linear problems since non-linearities in the system are carried down to the coarse levels through the re-discretization. <br />
<br />
==Restriction and Prolongation Operators ==<br />
<br />
Geometric multigrid requires restriction of both the fine grid solution and its residual or defect to coarse level. The restriction operator that transfers the solution to the next coarser grid level can be formed using a full-approximation scheme. In this, the solution for a coarse cell is obtained by taking the volume average of the solution values in the embedded fine grid cells. Or by other means of weighting. Residuals for the coarse grid cell are obtained simply by summing the residuals in the embedded fine grid cells.<br />
<br />
== Two grid Cycle ==<br />
The idea of geometric multigrid could be made clear by this two grid algorithm. <br><br />
<br />
:<math> a_P \phi _P = \sum\limits_{nb} {a_{nb} \phi _{nb} + s} </math> <br><br />
<br />
Then at fine level 2 <br><br />
:<math> <br />
a_P^2 \phi _P^2 = \sum\limits_{nb} {a_{nb}^2 \phi _{nb}^2 + s^2 } + r^2 <br />
</math><br />
this gives at coarse level 1 <br><br />
:<math> <br />
a_P^1 \phi _P^1 = \sum\limits_{nb} {a_{nb}^1 \phi _{nb}^1 + s^1 } + \left[ {\bar a_P^1 \bar \phi _P^1 - \sum\limits_{nb} {\bar a_{nb}^1 \bar \phi _{nb}^1 - \bar s^1 - \bar r^1 } } \right]<br />
</math><br />
<br />
Where <i> overbar </i> represents restricted variables.<br />
The additional source <math> \left[ {\bar a_P^1 \bar \phi _P^1 - \sum\limits_{nb} {\bar a_{nb}^1 \bar \phi _{nb}^1 - \bar s^1 - \bar r^1 } } \right] </math> does not change during the relaxations at coarse level.<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Geometric_multigrid_-_FASGeometric multigrid - FAS2005-10-03T08:32:48Z<p>Zxaar: </p>
<hr />
<div>==Geometric Multigrid or (FAS) ==<br />
In Geometric multigrid a hierarchy of meshes is generated.The discretized equations are evaluated on every level. The advantage of geometric multigrid over algebraic multigrid is that the former should perform better for non-linear problems since non-linearities in the system are carried down to the coarse levels through the re-discretization. <br />
<br />
==Restriction and Prolongation Operators ==<br />
<br />
Geometric multigrid requires restriction of both the fine grid solution and its residual or defect to coarse level. The restriction operator that transfers the solution to the next coarser grid level can be formed using a full-approximation scheme. In this, the solution for a coarse cell is obtained by taking the volume average of the solution values in the embedded fine grid cells. Or by other means of weighting. Residuals for the coarse grid cell are obtained simply by summing the residuals in the embedded fine grid cells.<br />
<br />
== Two grid Cycle ==<br />
The idea of geometric multigrid could be made clear by this two grid algorithm. <br><br />
<br />
:<math> a_P \phi _P = \sum\limits_{nb} {a_{nb} \phi _{nb} + s} </math> <br><br />
<br />
Then at fine level 2 <br><br />
:<math> <br />
a_P^2 \phi _P^2 = \sum\limits_{nb} {a_{nb}^2 \phi _{nb}^2 + s^2 } + r^2 <br />
</math><br />
this gives at coarse level 1 <br><br />
:<math> <br />
a_P^1 \phi _P^1 = \sum\limits_{nb} {a_{nb}^1 \phi _{nb}^1 + s^1 } + \left[ {\bar a_P^1 \bar \phi _P^1 - \sum\limits_{nb} {\bar a_{nb}^1 \bar \phi _{nb}^1 - \bar s^1 - \bar r^1 } } \right]<br />
</math><br />
<br />
Where <i> overbar </i> represents restricted variables.<br />
the additional source <math> \left[ {\bar a_P^1 \bar \phi _P^1 - \sum\limits_{nb} {\bar a_{nb}^1 \bar \phi _{nb}^1 - \bar s^1 - \bar r^1 } } \right] </math> does not change during the relaxations at coarse level.<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaarhttp://www.cfd-online.com/Wiki/Geometric_multigrid_-_FASGeometric multigrid - FAS2005-10-03T08:31:01Z<p>Zxaar: </p>
<hr />
<div>==Geometric Multigrid or (FAS) ==<br />
In Geometric multigrid a hierarchy of meshes is generated.The discretized equations are evaluated on every level. The advantage of geometric multigrid over algebraic multigrid is that the former should perform better for non-linear problems since non-linearities in the system are carried down to the coarse levels through the re-discretization. <br />
<br />
==Restriction and Prolongation Operators ==<br />
<br />
Geometric multigrid requires restriction of both the fine grid solution and its residual or defect to coarse level. The restriction operator that transfers the solution to the next coarser grid level can be formed using a full-approximation scheme. In this, the solution for a coarse cell is obtained by taking the volume average of the solution values in the embedded fine grid cells. Or by other means of weighting. Residuals for the coarse grid cell are obtained simply by summing the residuals in the embedded fine grid cells.<br />
<br />
== Two grid Cycle ==<br />
The idea of geometric multigrid could be made clear by this two grid algorithm. <br><br />
<br />
:<math> a_P \phi _P = \sum\limits_{nb} {a_{nb} \phi _{nb} + s} </math> <br><br />
<br />
Then at fine level 2 <br><br />
:<math> <br />
a_P^2 \phi _P^2 = \sum\limits_{nb} {a_{nb}^2 \phi _{nb}^2 + s^2 } + r^2 <br />
</math><br />
this gives at coarse level 1 <br><br />
:<math> <br />
a_P^1 \phi _P^1 = \sum\limits_{nb} {a_{nb}^1 \phi _{nb}^1 + s^1 } + \left[ {\bar a_P^1 \bar \phi _P^1 - \sum\limits_{nb} {\bar a_{nb}^1 \bar \phi _{nb}^1 - \bar s^1 - \bar r^1 } } \right]<br />
</math><br />
<br />
Where <i> overbar </i> represents restricted variables.<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaar