Designing optimal smoothers for multigrid methods for unsteady flow problems

We consider the solution of unsteady flow problems using multigrid methods. There, the typical solver comes from a dual time stepping approach, where an existing method designed for a steady problem is used for unsteady flows. This design mismatch leads to a significant decrease in convergence speed...

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Bibliographic Details
Published in20th AIAA Computational Fluid Dynamics Conference 2011
Main Author Birken, P.
Format Conference Proceeding
LanguageEnglish
Published 2011
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Summary:We consider the solution of unsteady flow problems using multigrid methods. There, the typical solver comes from a dual time stepping approach, where an existing method designed for a steady problem is used for unsteady flows. This design mismatch leads to a significant decrease in convergence speed. Here, we will use the linear advection equation as a model problem to find optimal Runge-Kutta smoothers specifically for the unsteady case, based on a Fourier analysis. This leads to a significantly improved multigrid method.
ISBN:1624101488
9781624101489
DOI:10.2514/6.2011-3233