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Algebraic multigrid methods for the solution of the Navier–Stokes equations in complicated geometries

✍ Scribed by Michael Griebel; Tilman Neunhoeffer; Hans Regler

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
400 KB
Volume
26
Category
Article
ISSN
0271-2091

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✦ Synopsis

The application of standard multigrid methods for the solution of the Navier±Stokes equations in complicated domains causes problems in two ways. First, coarsening is not possible to full extent since the geometry must be resolved by the coarsest grid used. Second, for semi-implicit time-stepping schemes, robustness of the convergence rates is usually not obtained for convection±diffusion problems, especially for higher Reynolds numbers. We show that both problems can be overcome by the use of algebraic multigrid (AMG), which we apply for the solution of the pressure and momentum equations in explicit and semi-implicit time-stepping schemes. We consider the convergence rates of AMG for several model problems and demonstrate the robustiness of the proposed scheme.

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