Volume 10, pp. 74-91, 2000.

A hybrid multigrid method for the steady-state incompressible Navier-Stokes equations

Michael Pernice

Abstract

Multigrid methods for solving the steady-state incompressible Navier-Stokes equations require an appropriate smoother and coarse grid solution strategy to be effective. Classical pressure-correction methods, such as SIMPLE and SIMPLER, are widely used as solvers in engineering analysis codes, but can also be used as effective multigrid smoothers. An inexact Newton method preconditioned by a linear multigrid method with a pressure-correction smoother can serve as a coarse grid solver. A hybrid nonlinear multigrid scheme based on combinations of these components is described. A standard benchmark problem is used to demonstrate the effectiveness of SIMPLER smoothing and the impact an inexact Newton coarse grid solver has on the resulting nonlinear multigrid scheme.

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Key words

multigrid, Newton-Krylov methods, pressure-correction methods, incompressible fluid dynamics.

AMS subject classifications

65N55, 65H10.

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