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

What is C.V. based finite element method

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

LinkBack Thread Tools Display Modes
Old   November 4, 1998, 12:56
Default What is C.V. based finite element method
C-H Kuo
Posts: n/a
From previous topics on FD vs.FV, Duane metioned the CV based finite element method a better approach for CFD. Can someone make more detailed description on this method?

As I know the major commercial CFD codes for handling multi-million element problems seem all based on FV method. From textbook I know FEM is more accurate than FV; however, FEM suffers from computing speed and large RAM when dealing with large number of elements.

It seems to me that differences among commercial FV codes are: accuracy due to various discretization schemes, the way of solving large sparse linear system, solution algorithm, and customization for specific engineering problem. Otherwise, I cannot expect too radical advantage from a certain code, such as computing speed or accuracy.

Would this CV based FEM achieves both accuracy and speed. I think many are wondering how and why.

  Reply With Quote

Old   November 4, 1998, 15:41
Default Re: What is C.V. based finite element method
Philip Zwart
Posts: n/a
A control-volume based finite volume method (CVFEM) is still a FV method, but defines the volumes differently from the more traditional FV method. in particular, the traditional method (some call it the "cell-centered method" chooses the volumes to be the same as the cells of the mesh. The CVFEM, on the other hand, chooses the volumes from a dual mesh; ie, there is one control volume associated with each vertex. The reason it is called a finite element method is that shape functions within the element can be used to help discretize the fluxes at the control volume faces. Thus the CVFEM is in some sense a marriage of the FV and FE methods. Other people call the same approach a "cell-vertex method" or "element-based finite volume method" or "vertex-centered finite volume method" etc.

Which is better is a matter of debate and personal preference. Some people like the fact that the CVFEM is related to the FE element method (in fact, in some canonical cases the discrete equations are identical to a Galerkin discretization.) What is interesting is the difference in unknowns, particularly on unstructured simplex meshes. In 2d, there are twice as many triangles as vertices, and in 3d there are 5-7 times as many tetrahedra as vertices. Thus the cell-centered approach may be expected to give better accuracy, but also more cost. Has anyone done a direct comparison?
  Reply With Quote

Old   November 4, 1998, 16:16
Default Re: What is C.V. based finite element method
C-H Kuo
Posts: n/a
So, Philip, let me interpret it in this way to see if I am getting right.

The integration over a CV is still same as traditional FVM, but the discretization of convection and diffusion terms on control surface is somehow complicated and more accurate. Actually, in unstructured polyhedral mesh, discretization on control surface is complicated and involves more neighbouring information than structure mesh. If shape function is implenmented in this stage, it should not affect solution scheme too much, or would it cause problem in stability and convergence?

OR, I am wrong. The two control volumes for both mesh and vertex should be formed in the global system to be solved?
  Reply With Quote

Old   November 5, 1998, 10:07
Default Re: What is C.V. based finite element method
Philip Zwart
Posts: n/a
I think you're on the right track, but I don't see the difference you're talking about for structured and unstructured meshes. Perhaps the best thing is to suggest some papers that deal with the subject.

For unstructured meshes, several papers by Tim Barth (I think they've been listed in some other threads, dealing with FV for unstructured meshes) are good. He uses an edge data structure to calculate the fluxes.

For structured meshes, there's the paper Schneider & Raw, "Control Volume Finite-Element Method for heat transfer and fluid flow using colocated variables -- 1. Computational procedure", Numerical Heat Transfer 11:363-390 (1987) which also references earlier work by Schneider & Zedan (for scalar transport) and Baliga & Patankar (for staggered grids). These papers use an element data structure to assemble the fluxes.

Hope this helps,

  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
Is Particle Finite Element Method applied in CFX? WenZyn Lim CFX 0 April 6, 2011 11:47
Finite element method in excel roger_1 Main CFD Forum 1 March 21, 2011 14:06
Finite element method - number of elements poornima Main CFD Forum 6 April 14, 2006 07:23
finite volume VS finite element solomon Main CFD Forum 0 March 19, 2002 20:04
Equations for finite difference, element & volume W.L.C. Main CFD Forum 9 April 3, 2001 12:08

All times are GMT -4. The time now is 21:43.