Monolithic Multigrid Methods for Magnetohydrodynamics

The magnetohydrodynamics equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. After discretization and linearization, the resulting...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2021-01, Vol.43 (5), p.S70-S91
Main Authors: Adler, James H., Benson, Thomas R., Cyr, Eric C., Farrell, Patrick E., MacLachlan, Scott P., Tuminaro, Ray S.
Format: Article
Language:English
Subjects:
magnetohydrodynamics
MATHEMATICS AND COMPUTING
monolithic multigrid
Vanka relaxation
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Summary:The magnetohydrodynamics equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. After discretization and linearization, the resulting system of equations is generally difficult to solve due to the coupling between variables and the heterogeneous coefficients induced by the linearization process. In this paper, we investigate multigrid preconditioners for this system based on specialized relaxation schemes that properly address the system structure and coupling. Here, three extensions of Vanka relaxation are proposed and applied to problems with up to 170 million degrees of freedom and fluid and magnetic Reynolds numbers up to 400 for stationary problems and up to 20,000 for time-dependent problems.
ISSN:1064-8275
1095-7197
DOI:10.1137/20M1348364