TY - JOUR
T1 - An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model
AU - Zhao , Jianping
AU - Chen , Rui
AU - Su , Haiyan
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 - <p style="text-align: justify;">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.</p>