Volume 13, Issue 4
An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model

Jianping Zhao, Rui Chen & Haiyan Su

Adv. Appl. Math. Mech., 13 (2021), pp. 761-790.

Published online: 2021-04

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  • 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.

  • Keywords

Magnetohydrodynamic equations, Cahn-Hilliard equation, finite element method, absolutely energy-stable, constant auxiliary variable.

  • AMS Subject Headings

65N02, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-761, author = {Jianping Zhao , and Rui Chen , and Haiyan Su , }, title = {An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0044}, url = {http://global-sci.org/intro/article_detail/aamm/18750.html} }
TY - JOUR T1 - An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model AU - Jianping Zhao , AU - Rui Chen , AU - Haiyan Su , JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 761 EP - 790 PY - 2021 DA - 2021/04 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0044 UR - https://global-sci.org/intro/article_detail/aamm/18750.html KW - Magnetohydrodynamic equations, Cahn-Hilliard equation, finite element method, absolutely energy-stable, constant auxiliary variable. AB -

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.

Jianping Zhao, Rui Chen & Haiyan Su. (1970). An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model. Advances in Applied Mathematics and Mechanics. 13 (4). 761-790. doi:10.4208/aamm.OA-2020-0044
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