Monolithic Multigrid for Magnetohydrodynamics

Abstract

The magnetohydrodynamics (MHD) 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. 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.

References in corpus (4)

• Robust Preconditioners for Incompressible MHD Models
• A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations
• PCPATCH: software for the topological construction of multigrid relaxation methods
• A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D

Cited by in corpus (1)

• An augmented Lagrangian preconditioner for the magnetohydrodynamics equations at high Reynolds and coupling numbers