Structure-preserving and efficient numerical simulation for diffuse interface model of two-phase magnetohydrodynamics

Abstract

In this paper, we propose a novel diffuse interface model of two-phase magnetohydrodynamics (MHD) based on a magnetic vector potential formulation in the three-dimensional case. This model ensures an exact divergence-free approximation of the magnetic field by introducing a magnetic vector potential A and defining the magnetic field by B=curlA. The resulting framework constitutes a highly coupled, nonlinear saddle point system consisting of the Cahn–Hilliard system and MHD potential system. To solve the model efficiently, we present two fully decoupled, first-order, linear, and unconditionally energy-stable schemes and strictly prove their well-posedness and energy stability. Finally, we present several numerical examples that demonstrate the stability and effectiveness of our schemes.