## [Libmesh-users] FE fluid flow algorithms

 [Libmesh-users] FE fluid flow algorithms From: Manav Bhatia - 2007-09-04 15:55:27 ```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. Are there other generic formulations that lead to a single system of equations instead of a multistep algorithm? How do these match-up against this CBS-Galerkin algorithm? Please recommend some good references if possible. Regards, Manav ```

 [Libmesh-users] FE fluid flow algorithms From: Manav Bhatia - 2007-09-04 15:55:27 ```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. Are there other generic formulations that lead to a single system of equations instead of a multistep algorithm? How do these match-up against this CBS-Galerkin algorithm? Please recommend some good references if possible. Regards, Manav ```