A fully discretization, unconditionally energy stable finite element method solving the thermodynamically consistent diffuse interface model for incompressible two-phase MHD flows with large density ratios

A diffusion interface two-phase magnetohydrodynamic model has been used for matched densities in our previous work [1,2], which may limit the applications of the model. In this work, we derive a thermodynamically consistent diffuse interface model for diffusion interface two-phase magnetohydrodynamic fluids with large density ratios by Onsager's variational principle and conservation law for the first time. The finite element method for spatial discretization and the first order semi-implicit scheme linked with convect splitting method for temporal discretization, is proposed to solve this new model. The mass conservation, unconditionally energy stability and convergence of the scheme can be proved. Then we derive the existence of weak solutions of governing system employing the above properties of the scheme and compactness method. Finally, we show some numerical results to test the effectiveness and well behavior of proposed scheme.