Second-order energy stable schemes for the new model of the Cahn-Hilliard-MHD equations (Q2025439)

The authors propose the CHiMHD (Cahn-Hilliard equations and the inductionless magnetohydrodynamic equations) model which couples the Cahn-Hilliard equations and the inductionless, incompressible MHD equations for two-phase flows. The model can be used to simulate the dynamic behavior of two-phase conducting fluids under the influence of magnetic field. To resolve the problem, two fully discrete time-marching schemes which are linear, decoupled, unconditionally energy stable, and of second order are established. Several numerical tests are presented to justify the second-order convergence of the numerical methods. The article is interesting and deserves to be read.