Higher‐order finite element discretizations in a benchmark problem for incompressible flows

Abstract

AbstractWe present a numerical study of several finite element discretizations applied to a benchmark problem for the two‐dimensional steady state incompressible Navier–Stokes equations defined in Schäfer and Turek (The benchmark problem ‘Flow around a cylinder’. In Flow Simulation with High‐Performance Computers II. Notes on Numerical Fluid Mechanics, vol. 52, Hirschel EH (ed.). Vieweg: Wiesbaden, 1996; 547–566). The discretizations are compared with respect to the accuracy of the computed benchmark parameters. Higher‐order isoparametric finite element discretizations turned out to be by far the most accurate. The discrete systems obtained with higher‐order discretizations are solved with a modified coupled multigrid method whose behaviour within the benchmark problem is also studied numerically. Copyright © 2001 John Wiley & Sons, Ltd.