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Concerning a general CFD unstructured grid case, what is the most efficient matrix solver so far or in the near future that can solve the matrix really fast with thousands of CPUs.

I am using OpenFOAM to do the simulation of incompressible flow. It uses OpenMPI to run the parallel jobs. The simulation is 2D or 3D, and uses a finite volume discretization. I'd like to run very large case studies, with around 10 million to 1 billion grid points. For these case studies, I need the solution over a long time interval.

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Daniel, welcome to SciComp! Could you provide us with some more information? Is your CFD simulation in 1D, 2D, or 3D? How are you discretizing the PDEs? (Finite difference, finite element, finite volume...?) Additional information will help us write better answers that are tailored to your particular problem. – Geoff Oxberry♦ May 30 '12 at 22:21
Additionally, is this compressible or incompressible flow? Specifically, what system is being treated implicitly? How are you managing parallelism? There is a plethora of methods so you will have to provide quite a bit of detail for us to offer specific advice. – Jed Brown May 30 '12 at 22:56
Thanks! I am using OpenFOAM to do the simulation of incompressible flow. It uses openmpi to run the parallel jobs. The simulation is 2D or 3D, OpenFOAM is finite volume code. – Daniel May 31 '12 at 20:17
Daniel, I edited the question to incorporate your comments. Please let me know if I misinterpreted anything. – Geoff Oxberry♦ Jun 1 '12 at 18:49
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I happen to know enough about the default time splitting methods used by OpenFOAM for incompressible flow (assuming it hasn't changed in the last couple years), but that really needs to go into the question. You should write a paragraph or two explaining what system is being solved and what method you are currently using. It would also be helpful to indicate how much effort you are willing to put in to implement a method that isn't already in the suite. – Jed Brown Jun 1 '12 at 19:38

migrated from math.stackexchange.com May 30 '12 at 22:09

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