CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

Meshless FD method over FEM?

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   April 17, 2004, 23:39
Default Meshless FD method over FEM?
Posts: n/a
Hi all,

Recent meshless methods are proving to be a better way of solving nonlinear equations in CFD. I have used Least Square based Finite Difference and it proved to be a great tool.

I have read in many discussions that FD has a disadvantage that it cant be applied to complex geometries. Now, I have a doubt with this. If FD can solve complex geometries easily, does it mean that meshless FD is better than FEM?

(In Least Square Based FD, the derivatives can be approximated to a higher order easily)

Please clarify,

Regards, Shyam
  Reply With Quote

Old   April 30, 2004, 11:09
Default Re: Meshless FD method over FEM?
Posts: n/a
Hi, Shyam:

Could you introduce some reference on meshless FD?


- Ma

  Reply With Quote

Old   May 5, 2004, 02:35
Default Re: Meshless FD method over FEM?
Posts: n/a
Here is a list of references on meshless methods in CFD. There is a growing body of literature in structural mechanics, see IJNME, JNMF, and Comp. Meth. Appl. Mech. Engg.

<h3> Some references on Meshless Methods </h3>
  1. T Liszka, "An interpolation method for an irregular net of nodes", Int. Jl. for Num. Meth. in Engg., 20:1599-1612, 1984.
  2. T Liszka and J Orkisz, "The finite difference method at arbitrary irregular grids and its application in applied mechanics'', Comp. Struct., 11:83-95, 1980.
  3. KC Chung, "A generalised finite difference method for heat transfer problems of irregular geometries'', Num. Heat Transfer, 4:345-357, 1981.
  4. EJ Kansa (1990): "Multiquadrics- A scattered data approximation scheme with applications to computational fluid dynamics: II. Solutions to parabolic, hyperbolic and elliptic partial differential equations", Comput. Math. Appl., 19(6-8):147-161.
  5. JT Batina, "A gridless Euler/Navier-Stokes solution algorithm for complex aircraft applications'', AIAA Paper 93-0333, 1993.
  6. T Belytschko, YY Lu, and L Gu, "Element-free Galerkin methods", Int. Jl. Num. Meth. Engg., 37:229-256, 1994.
  7. AK Ghosh, SM Deshpande, "Least squares kinetic upwind method for inviscid compressible flows'', AIAA paper 95-1735,1995.
  8. Yagawa G and Yamada T, "Free mesh method: A new meshless finite element method'', Comp. Mech., 18:383-386, 1996.
  9. T Belytschko, Y Krongauz, D Organ, M Flemming and P Krysl, "Meshless methods: An overview and recent developments", Comput. Methods Appl. Mech. Engg., Vol. 139, pp. 3-47, 1996. (This contains a comprehensive review of many meshless techniques.)
  10. K Morinishi (1999): "An implicit gridless type solver for the Navier-Stokes equations'', Int. Symp. on CFD, Bremen.
  11. H Wendland (1999): "Meshless Galerkin methods using radial basis functions", Math. Comp., 68:1521-1531.
  12. M Junk, "Do finite volume methods really need a mesh ?", Int. Workshop on Meshfree Methods for PDE, Bonn, September, 2001.
  13. R Lohner, C Sacco, E Onate and S Idelsohn (2002): "A finite point method for compressible flows'', Int. Jl. Num. Meth. Engg., Vol. 53, pp. 1765-1779.
  14. Michael Griebel and Marc Schweitzer, ed. (2002): Meshfree methods for Partial Differential Equations, LNCSE, Springer, 2002.
  15. G.R. Liu: Meshfree Methods - Moving beyond the Finite Element Method , 712 pages, 2002, CRC Press. ISBN: 0849312388. (This is the first textbook on meshless methods, and till now the only one that I am aware of.)
  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
Lattice Boltzmann method vs Finite Element Method and Finite Volume Method solemnpriest Main CFD Forum 3 August 12, 2013 11:00
discretizer - gmshToFoam Andyjoe Open Source Meshers: Gmsh, Netgen, CGNS, ... 13 March 14, 2012 05:35
Code for most powerfull FDV Method D.S.Nasan Main CFD Forum 6 September 4, 2008 02:08
Penalty method and FEM John Main CFD Forum 0 July 9, 2005 17:44
comments on FDM, FEM, FVM, SM, SEM, DSEM, BEM kenn Main CFD Forum 2 July 18, 2004 18:28

All times are GMT -4. The time now is 02:27.