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.