Fully Decoupled, Linear and Unconditionally Energy Stable Time Discretization Scheme for Solving the Magneto-Hydrodynamic Equations

Abstract

In this paper, we consider numerical approximations for solving the magneto-hydrodynamic equations, which couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is the time discretization, i.e., how to develop suitable temporal discretizations for the nonlinear terms in order to preserve the energy stability at the discrete level. We solve this issue in this paper by developing a linear, fully decoupled first order time marching scheme, by combining the projection method for Navier-Stokes equations and some subtle implicit—explicit treatments for nonlinear coupling terms. We further prove that the scheme is unconditional energy stable and derive the optimal error estimates of the semi-discretization rigorously. Various numerical simulations are implemented to demonstrate the stability and the accuracy.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Comments

Xiaoming He's research is partially supported by the U.S. National Science Foundation under Grant Numbers DMS-1722647 and DMS-1818642.

Keywords and Phrases

Decoupled; Error Estimates; First Order; Linear; Magneto-Hydrodynamics; Unconditional Energy Stability

International Standard Serial Number (ISSN)

0377-0427

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2020 Elsevier B.V., All rights reserved.

Publication Date

01 May 2020

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