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Finite Element vs. Finite Volume Codes

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Old   December 22, 2005, 13:53
Default Finite Element vs. Finite Volume Codes
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Salman
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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.
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Old   December 22, 2005, 13:56
Default Re: Finite Element vs. Finite Volume Codes
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tiger
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Most CFD people use the finite volume because of it's stability over the finite element.
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Old   December 22, 2005, 21:19
Default Re: Finite Element vs. Finite Volume Codes
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diaw
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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...
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Old   December 26, 2005, 21:07
Default Re: Finite Element vs. Finite Volume Codes
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zxaar
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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.
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Old   December 29, 2005, 02:45
Default Re: Finite Element vs. Finite Volume Codes
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Hubert Janocha
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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
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Old   January 2, 2006, 20:14
Default Re: Finite Element vs. Finite Volume Codes
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Salman
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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.
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Old   January 3, 2006, 10:26
Default Re: Finite Element vs. Finite Volume Codes
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diaw
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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...
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Old   January 3, 2006, 14:58
Default Finite elemnent and finite volume
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S. Dhinakaran
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Finite volume codes are easy to write. Writing a finite element code is laborious and it takes much time.
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Old   January 6, 2006, 05:19
Default Re: Finite elemnent and finite volume
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Alex Muthaiah
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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
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Old   January 6, 2006, 23:59
Default Re: Finite elemnent and finite volume
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diaw
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>>>1)Finite Element basically works on Weighted residual method and Finite Volume works bascially on Conservation priniciples.

--------

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

diaw...
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