CFD using Finite Elements
Hi
I am planning on working on a FE based CFD solution for compressible flows. Being new to CFD, I started with the third volume of Zienkiewicz's book "Finite Element Method" where he has described a CBS algorithm. In the book, the authors have strongly advocated its use, and say that this is a generic algorithm and can be used for any kind of flow. The algorithms consists of 4 steps: step1: approximate new mass flux using the momentum equations step2: calculate new pressures step3: correct mass flux step4: solve energy equations This algorithm involves solving multiple systems of equations. I have a few questions:  Has anyone on this mailing list had any experience with this algorithm?  As I understand, the multiple steps arise out of an attempt to obtain the optimal variational formulation of the PDEs so that simple Galerkin discretization could be used. This is obtained by employing a characteristic based flux split. What other generic formulations lead to a single system of equations instead of a multistep algorithm? How do these matchup against this CBSGalerkin algorithm? Regards, Manav 
Re: CFD using Finite Elements
I dont know enough to give you a comparison but for compressible flows, you may want to check out SUPG finite element method and discontinuous galerkin method.

Re: CFD using Finite Elements
I tried to do like the way you mentioned. But the FE is not good enough to capture the shock in compressible flow. The way I accomplised was the fluxcorrected transport. It showed a shockcaptured profile but too diffusive compared to the FV approximation. Now, I am using the discontinuous Galerkin method(DGM) which is the combination of advantages of FE and FV. Its performace was superior to any FE approximation in the simulation of compressible flow. Any FEbased compressible flow solver must be not better than the FVbased compressible flow. Try the DGM or FV for compressible fluid flow if you want to get the sharp shock capturing.

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