An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model
Year: 2021
Author: Jianping Zhao, Rui Chen, Haiyan Su
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 761–790
Abstract
In this paper, we present an efficient energy stable finite element method for the two phase incompressible Magnetohydrodynamic (MHD) flow which is governed by the incompressible MHD equations and the Cahn-Hilliard equation. The strong nonlinear system governs the dynamics and the coupling of multiple physical fields which are, respectively, the velocity $\mathbf{u}$, the pressure $p$, the magnetic induction $\mathbf{B}$, the concentration $\phi$, and the chemical potential $\mu$. To solve the problem efficiently, we propose a linearized finite element scheme which is absolutely stable in time. Several numerical experiments are shown for demonstrating the competitive behavior of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0044
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 761–790
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Magnetohydrodynamic equations Cahn-Hilliard equation finite element method absolutely energy-stable constant auxiliary variable.
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