Premium
Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier–Stokes equations
Author(s) -
John Volker
Publication year - 2002
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.377
Subject(s) - multigrid method , benchmark (surveying) , solver , finite element method , discretization , generalized minimal residual method , mathematics , navier–stokes equations , preconditioner , computational fluid dynamics , saddle point , computer science , mathematical optimization , iterative method , partial differential equation , mathematical analysis , geometry , physics , mechanics , compressibility , geodesy , thermodynamics , geography
This paper presents a numerical study of the 3D flow around a cylinder which was defined as a benchmark problem for the steady state Navier–Stokes equations within the DFG high‐priority research program flow simulation with high‐performance computers by Schafer and Turek (Vol. 52, Vieweg: Braunschweig, 1996). The first part of the study is a comparison of several finite element discretizations with respect to the accuracy of the computed benchmark parameters. It turns out that boundary fitted higher order finite element methods are in general most accurate. Our numerical study improves the hitherto existing reference values for the benchmark parameters considerably. The second part of the study deals with efficient and robust solvers for the discrete saddle point problems. All considered solvers are based on coupled multigrid methods. The flexible GMRES method with a multiple discretization multigrid method proves to be the best solver. Copyright © 2002 John Wiley & Sons, Ltd.