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Error Analysis of a New Euler Semi-Implicit Time-Discrete Scheme for the Incompressible MHD System with Variable Density

Error Analysis of a New Euler Semi-Implicit Time-Discrete Scheme for the Incompressible MHD System with Variable Density

Year:    2025

Author:    Yuan Li, Xuewei Cui

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 263–294

Abstract

The incompressible magnetohydrodynamics system with variable density is coupled by the incompressible Navier-Stokes equations with variable density and the Maxwell equations. In this paper, we study a new first-order Euler semi-discrete scheme for solving this system. The proposed numerical scheme is unconditionally stable for any time step size $\tau>0.$ Furthermore, a rigorous error analysis is presented and the first-order temporal convergence rate $\mathcal{O}(\tau)$ is derived by using the method of mathematical induction and the discrete maximal $L^p$-regularity of the Stokes problem. Finally, numerical results are given to support the theoretical analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2023-0025

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 263–294

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:    Magnetohydrodynamics variable density flows Euler semi-implicit scheme error analysis.

Author Details

Yuan Li

Xuewei Cui