An Efficient Nonlinear Solver for Steady MHD Based on Algebraic Splitting

An Efficient Nonlinear Solver for Steady MHD Based on Algebraic Splitting

Year:    2021

Author:    Mengying Xiao

International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 5 : pp. 674–689

Abstract

We propose a new, efficient, nonlinear iteration for solving the steady incompressible MHD equations. The method consists of a careful combination of an incremental Picard iteration, Yosida splitting, and a grad-div stabilized finite element discretization. At each iteration, the Schur complement remains the same, is SPD, and can be easily and effectively preconditioned with the pressure mass matrix. Furthermore, this method decouples the block Schur complement into 2 simple Stokes Schur complement. We show that the iteration converges linearly to the discrete MHD system solution, both analytically and numerically. Several numerical tests are given which reveal very good convergence properties, and excellent results on a benchmark problem.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2021-IJNAM-19388

International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 5 : pp. 674–689

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Steady MHD algebraic splitting incremental Picard Yosida method nonlinear solver.

Author Details

Mengying Xiao