Decoupled, linear, unconditionally energy stable and charge-conservative finite element method for an inductionless magnetohydrodynamic phase-field model

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics (MHD) problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and Poisson equation. We propose a linear and decoupled finite element method to solve this highly nonlinear and multi-physics system. For the time variable, the discretization is a combination of the first order Euler semi-implicit scheme, several first-order stabilization terms and implicit-explicit treatments for coupling terms. For the space variables, we adopt the finite element discretization. Especially, we approximate the current density and electric potential by inf-sup stable face-volume mixed finite element pairs. With these techniques, the scheme only involves a sequence of decoupled linear equations to solve at each time step. We show that the scheme is provably mass-conservative, charge-conservative and unconditionally energy stable. Numerical experiments are performed to illustrate the properties, accuracy and efficiency of the proposed scheme. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.