Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:369

Article

Zhang, Guo-Dong¹  He, Xiaoming²  Yang, Xiaofeng³ 

[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Shandong, Peoples R China

[2] Missouri Univ Sci & Technol, Dept Math, Rolla, MO 65409 USA

[3] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

关键词: Magneto-hydrodynamics;    Linear;    Decoupled;    Unconditional energy stability;    First order;    Error estimates;   

DOI  :  10.1016/j.cam.2019.112636

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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