A fully decoupled linearized and second-order accurate numerical scheme for two-phase magnetohydrodynamic flows

Abstract

In this paper, we analyze the numerical approximation of two-phase magnetohydrodynamic flows. Firstly, an equivalent new system is designed by introducing two scalar auxiliary variables. One of variables is used to linearize the phase field function and the other is used to deal with the highly coupled and nonlinear terms. Secondly, by combining with a novel decoupling technique based on the “zero-energy-contribution” feature and the pressure correction method, the linearized second order BDF numerical scheme, which has the advantage of fully decoupled structure, is constructed. Furthermore, we strictly prove the unconditional energy stability and error analysis of the scheme, and give a detailed implementation procedure that only requires to calculate several linear elliptic equations with constant coefficients. Finally, the results of numerical simulations are presented to validate the rates of convergence and energy stability.