Abstract
We consider in this paper numerical approximations of two-phase incompressible flows with different densities and viscosities. We present a variational derivation for a thermodynamically consistent phase-field model that admits an energy law. Two decoupled time discretization schemes for the coupled nonlinear phase-field model are constructed and shown to be energy stable. Numerical experiments are carried out to validate the model and the schemes for problems with large density and viscosity ratios.
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