Monolithic Multigrid for Magnetohydrodynamics

06/28/2020
by   J. H. Adler, et al.
0

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.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

04/30/2021

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

The magnetohydrodynamics (MHD) equations are generally known to be diffi...
12/18/2019

PCPATCH: software for the topological construction of multigrid relaxation methods

Effective relaxation methods are necessary for good multigrid convergenc...
07/30/2019

A virtual element method for the miscible displacement of incompressible fluids in porous media

In the present contribution, we construct a virtual element (VE) discret...
02/15/2022

Monolithic multigrid for implicit Runge-Kutta discretizations of incompressible fluid flow

Most research on preconditioners for time-dependent PDEs has focused on ...
04/05/2021

A decision-making machine learning approach in Hermite spectral approximations of partial differential equations

The accuracy and effectiveness of Hermite spectral methods for the numer...
11/08/2021

Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes

Solutions to many partial differential equations satisfy certain bounds ...
03/29/2022

A Multigrid Preconditioner for Spatially Adaptive High-order Meshless Method on Fluid-solid Interaction Problems

We present a monolithic geometric multigrid preconditioner for solving f...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.