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Old   September 30, 2007, 22:22
Default FEM vs finite-differences
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I just starting to work with a project and free to choose a computational method which I'll use in my code.

I may be wrong but I think that it would be better to use FEM if one wants to solve RANS eqs for a flow with strong shocks and complex geometry. I expect the solution to belong W2 but not C2, so it's not smooth enough for finite-differences and will converge only in a "weak" sence.

What is Your professional opinion, FEM or FDM? If FDM, continuous or discrete? Does FEM require much more CPU time than Finite-Difference Method (for strong shocks)?

Thank You!

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Old   October 1, 2007, 08:58
Default Re: FEM vs finite-differences
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You've not considered Finite Volume Method (FVM)? This has the potential for capturing strong shocks and enforces the unlying conservation laws.
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Old   October 1, 2007, 13:04
Default Re: FEM vs finite-differences
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I think You are right. Finite volumes would be the best choise for flow with strong shocks. Thank You very much for advice! //natalie
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Old   October 1, 2007, 14:31
Default Re: FEM vs finite-differences
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with simple walk in literature, u see that fdm, fem or fvm could solve PDE with discintinuty or singularity, previously FDM has limitation to resolve complex geometry, that with appearance of local refinement/immersed bc/multiblock it is almost resolved, also fem had conservation problem which is resolved by appearence discontinuous galerkin based methods, ...

so selection of method seems to be arbitrary (only implementation difficulty and computational cost is issue !)

in my opinion: FEM is more easy to implement, particularly for a general solver, but it almost needs more computational cost, also mathematical theory and related open source codes of FEM have more matuarity which is another interesting issue.

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