Energy stable schemes with second order temporal accuracy and decoupled structure for diffuse interface model of two-phase magnetohydrodynamics

Abstract

In this paper, two second-order accurate in time, linear, decoupled and unconditionally energy stable schemes for the diffuse interface model of two-phase magnetohydrodynamics (MHD) are presented. The given schemes combine invariant energy quadratization (IEQ) method for the phase-field equations, second order type pressure projection method for the double saddle points MHD system, and some subtle implicit–explicit treatments for nonlinear coupled terms. The strongly coupled, highly nonlinear and double saddle points type two-phase MHD model is spilt into several smaller elliptic type problems, which can be solved efficiently. Rigorous proofs of the unconditional energy stabilities are provided in both temporal discretization and full discretization with finite element method in space approximation. Finally, various numerical results are presented to verify the accuracy and stability of the proposed schemes.