  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.
