A highly parallel code for strongly coupled fluid-transport equations

Conference paper (2014)

Authors

Weiyan Song University Medical Center Groningen
Fred W. Wubs University Medical Center Groningen
J. Thies German Aerospace Center
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Numerical methods High performance computing Multilevel ILU Multiphysics problems
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Published Date

01-07-2014

Language

English

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Abstract

We developed a finite volume package FVM and a solver HYMLS, both based on elements of the Trilinos EPETRA-package (see http://trilinos.sandia.gov/). HYMLS is a linear system solver for steady state incompressible Navier-Stokes equations coupled to transport equations in 2 and 3D [1, 2, 3]. We constructed recently a multilevel variant of it, which makes it possible to solve 3D problems of over 10 million unknowns quickly on a parallel computer. The behavior of the method is very much like that of multigrid methods. In fact one could see it as the father of the multigrid method. The solver is very robust. For the problem described in [4], it allowed a quick increase in the Reynolds number to get into the interesting region around Re=2000. Here we will show the performance of the method on the Rayleigh-Bénard convection in a cube, with six no-slip walls [5]. Also here we employ HYMLS to solve the linear systems resulting from a Cayley transform of the generalized eigenvalue problem.