Error Analysis of Second‐Order Decoupled Scheme for Two‐Phase Magnetohydrodynamic Diffuse Interface Model

ABSTRACT In this paper, we construct error analysis of second‐order decoupled scheme for the two‐phase magnetohydrodynamic diffuse interface model. First, we construct a second‐order time‐discrete scheme in which the time derivative term is treated by the second‐order backward difference formulation, the scalar auxiliary variable (SAV) method is used to linearize the nonlinear energy potential, and the other nonlinear terms are treated by semi‐implicit method. Importantly, we use Gauge–Uzawa method to decouple velocity and pressure. The proposed scheme have two distinct features: It does not need to give an initial value of the pressure; it does not require artificial boundary conditions on pressure, thus saving additional computational cost. Second, the unconditional stability of the second‐order scheme is proved. Then, through rigorous error analysis, we provide suboptimal convergence orders. Finally, some numerical experiments demonstrate the accuracy and effectiveness of the proposed scheme. It is also proved that the proposed scheme is superior to other classical second‐order scheme.