An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model

被引:14
作者
Zhao, Jianping [1 ]
Chen, Rui [2 ]
Su, Haiyan [1 ]
机构
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
[2] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China
关键词
Magnetohydrodynamic equations; Cahn-Hilliard equation; finite element method; absolutely energy-stable; constant auxiliary variable; DIFFUSE INTERFACE MODEL; ITERATIVE METHOD; SPECTRAL METHOD; STATIONARY; EQUATION; FIELD; TIME; APPROXIMATIONS; RECONNECTION; 2ND-ORDER;
D O I
10.4208/aamm.OA-2020-0044
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 u, the pressure p, the magnetic induction 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.
引用
收藏
页码:761 / 790
页数:30
相关论文
共 53 条
[1]  
Ames W.F, 2014, Numerical methods for partial differential equations
[2]   A 3D numerical simulation of mixed convection of a magnetic nanofluid in the presence of non-uniform magnetic field in a vertical tube using two phase mixture model [J].
Aminfar, Habib ;
Mohammadpourfard, Mousa ;
Kahnamouei, Yousef Narmani .
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS, 2011, 323 (15) :1963-1972
[3]  
[Anonymous], 1998, MRS ONLINE P LIB OPL
[4]  
[Anonymous], 2013, ENERGY METHOD STABIL
[5]  
[Anonymous], 2003, SOBOLEV SPACES
[6]  
Babuska I., 2012, Modeling, mesh generation, and adaptive numerical methods for partial differential equations, V75
[7]  
Bateman G., 1978, MHD INSTABILITIES
[8]   Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows [J].
Cai, Yongyong ;
Choi, Heejun ;
Shen, Jie .
NUMERISCHE MATHEMATIK, 2017, 137 (02) :417-449
[9]   ORDER-N SPECTRAL METHOD FOR ELECTROMAGNETIC-WAVES [J].
CHAN, CT ;
YU, QL ;
HO, KM .
PHYSICAL REVIEW B, 1995, 51 (23) :16635-16642
[10]  
CHEN HONGTAO, 2020, NATURE, P1