
[Sponsors] 
May 25, 2010, 09:53 
3D Stream Function

#1 
New Member
Mohsen
Join Date: May 2010
Posts: 1
Rep Power: 0 
Dear Friends,
I am solving 2D Navier Stocks equation in Biharmonic formulation. But now I want to know that is it possible to solve this equation in 3D ? Indeed the Biharmonic equations in 2D come from Stream FunctionVorticity method. We know that we don't have Stream Function Vorticity in 3D space But we have 3D operator for Biharmonic equation. Email: mlashckar@yahoo.com Many Thanks M.Lashckar 

May 26, 2010, 10:09 

#3 
Member
private
Join Date: Mar 2009
Posts: 74
Rep Power: 10 
Actually the stream function and vorticity are vectors.
In a twod problem, each vector has only one component. In a threed problem, each vector has 3 components, and the biharmonic equation becomes three biharmonic equations. Instead of a twoscalar (stream function and vorticity) one solves for six scalars (three for the stream function vector and three for the vorticity vector). Probably someone has tried to solve such a system. 

May 28, 2010, 02:42 

#4 
Member
adrin
Join Date: Mar 2009
Posts: 82
Rep Power: 10 
the problem of a vectorial poisson equation for the "stream function" with vectorial vorticity as its source is at the heart of Lagrangian vortex particle methods and is routinely solved in its integral form (Biot Savart formula). I have also seen at least one paper where the "streamfunction"vorticity method is solved in 3D using finite difference methods (I forget the author now).
adrin 

October 29, 2010, 08:26 

#5 
New Member
hari
Join Date: Oct 2010
Posts: 1
Rep Power: 0 
hi i am hari.
iam not fimililar with these stream function & velocity potential. why we have 2 use these. what is the use of these things... 

October 29, 2010, 16:44 

#6 
New Member
Join Date: Jun 2010
Posts: 16
Rep Power: 9 
Hi,
There exist 3D stream functions (two functions). See, for example, R. G. Campbell, Foundaitons of Fluid Flow Theory, AddisonWesley, 1973. Here is a paper on the application of 3D stream functions to CFD: A. Sherif and M. Hafez, Computation of threedimensional transonic flows by using two stream functions. International Journal for Numerical Methodsin Fluids, 8, 1729, 1988. http://onlinelibrary.wiley.com/doi/1...80103/abstract bjohn 

March 22, 2016, 06:31 

#7 
New Member
Wang Zhe
Join Date: Apr 2015
Location: Singapore
Posts: 10
Rep Power: 4 
I have found this in the physic forums regarding a similar question:
"For the case of 3d flows, it is possible to use two stream functions to replace the continuity equation. However, the complexity of this approach usually makes it less attractive than using the continuity equation in its original form." Reference https://www.physicsforums.com/thread...unction.84860/ 

March 22, 2016, 10:26 

#8  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,418
Rep Power: 39 
Quote:
formally, the stream functionvorticity formulation in 3D in nothing else the solution of the Helmholtz equation in vector form (3 scalar functions for the vorticity) coupled with the Poisson equation for the potential vector field Psi (a stream function is denoted only for 2D). Owing to the 3 Poisson equations for the scalar fields Psi_i this formulation is not appealing. However, some proposal in literature used to simplify the number of scalar functions. Let me say that, the formulation in terms of vorticity is quite complex if one solves turbulence, the closure model for the vorticity field and the BC.s are much less studied than they are for the velocitypressure formulation. 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Compile problem  ivanyao  OpenFOAM Running, Solving & CFD  1  October 12, 2012 09:31 
BlockMesh FOAM warning  gaottino  OpenFOAM Native Meshers: blockMesh  7  July 19, 2010 14:11 
latest OpenFOAM1.6.x from git failed to compile  phsieh2005  OpenFOAM Bugs  25  February 9, 2010 05:37 
Error with Wmake  skabilan  OpenFOAM Installation  3  July 28, 2009 00:35 
Axisymmetrical mesh  Rasmus Gjesing (Gjesing)  OpenFOAM Native Meshers: blockMesh  10  April 2, 2007 14:00 