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-   -   Finite Element vs. Finite Volume Codes (https://www.cfd-online.com/Forums/main/10519-finite-element-vs-finite-volume-codes.html)

 Salman December 22, 2005 13:53

Finite Element vs. Finite Volume Codes

Can anybody explain to me the difference between finite element and finite volume CFD codes? Which one is preferable for what type of problems? Thanks.

 tiger December 22, 2005 13:56

Re: Finite Element vs. Finite Volume Codes

Most CFD people use the finite volume because of it's stability over the finite element.

 diaw December 22, 2005 21:19

Re: Finite Element vs. Finite Volume Codes

I have found that the FEM showcases the underlying physics in a superior way to FVM, which tends to, by its cell-averaging design, damp certain physical phenomena.

The nodal interconnectivity of FEM gives useful inter-node information.

I understand that there is information in the Wiki on the FVM - FEM comparison.

diaw...

 zxaar December 26, 2005 21:07

Re: Finite Element vs. Finite Volume Codes

on Wiki on the FVM - FEM comparison is still not written, i wished to add but i do not understant much of FEM, so left it for people who excel in FEM.

 Hubert Janocha December 29, 2005 02:45

Re: Finite Element vs. Finite Volume Codes

FEM is normaly apllied to structurall analysis, because the code calculates a length expansion, and out of this it calculates the stress as the first derivation of the length. To be able to do this the FEM-Cell must have at least a linear weight function, which means there are two points discribing a line (e.g. in 3D 8 nodes per hexaeder-cell). The fist derivation of it is a constant function. When you have for e.g. a 1D problem, you would get a piecewise (per dx-interval) constant stairways shape of the stress, which is not really accurate. So you better choose a quadratic weight function (means in 1D there are 3 points defining a quadratic funtion), to get a linear stress in the dx-intervall. For a first shot many peaple using the linear cells in combination with a higher mesh resolution.

In CFD there is no need to calculate a first derivation of a value. Because of this a constant weight function is sufficient (FV-Methode, only 1 node per cell). You can increase the result accuracy by using FE-Methods, but is has a great overhead, which let dramatically decrease the speed of the solution progress. To manage at least 8 nodes per cell (linear wight function) instead of only 1 node per cell leads to a extrem memory requirement.

Conclusion: In Structural analysis you don't have a choice, you have to use at least a linear cell, because of the first derivation of the length. But in CFD, (especially for large meshes and in transient calculations) FEM-Methods are not really practicable, in these days (!).

By the way; when using more and smaller cells in general, the needed geometrical accuracy given by the modell-walls (especially in CFD) is much higher.

Hope this helps Hubert Janocha

 Salman January 2, 2006 20:14

Re: Finite Element vs. Finite Volume Codes

Thanks for all your replies. Some CFD packages that use FEM approach, present it as part of the natural evolution of things. Now I have a better idea.

 diaw January 3, 2006 10:26

Re: Finite Element vs. Finite Volume Codes

For fluids, FEM will provide intricate flow details that FVM would be hard-pressed to do. The interconnectivity between nodes is precisely why FEM does such a good job. I think of FVM as a glorified form of FDM - a net of point samplings taken over the flow domain.

diaw...

 S. Dhinakaran January 3, 2006 14:58

Finite elemnent and finite volume

Finite volume codes are easy to write. Writing a finite element code is laborious and it takes much time.

 Alex Muthaiah January 6, 2006 05:19

Re: Finite elemnent and finite volume

1)Finite Element basically works on Weighted residual method and Finite Volume works bascially on Conservation priniciples.

2)In FEM nodal connectivity is important to get solution if u r not able to make so it will take as freeedge in solution domain. But in FVM nodal connectivity is not mandatory but face connectivity is must since flux b/t cell face has to conserve.

ciyo

Alex

 diaw January 6, 2006 23:59

Re: Finite elemnent and finite volume

>>>1)Finite Element basically works on Weighted residual method and Finite Volume works bascially on Conservation priniciples.

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FVM is also a Weighted Residual method... with constant weighting (ref Patankar - p30)

diaw...

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