Numerical Approximations for Allen-Cahn Type Phase Field Model of Two-Phase Incompressible Fluids with Moving Contact Lines (Communications in Computational Physics, 2018)
In this paper, we present some efficient numerical schemes to solve a two-phasehydrodynamics coupled phase field model with moving contact line boundaryconditions. The model is a nonlinear coupling system, which consists the Navier-Stokesequations with the general Navier Boundary conditions or degenerated NavierBoundary conditions, and the Allen-Cahn type phase field equations with dynamicalcontact line boundary condition or static contact line boundary condition. The proposedschemes are linear and unconditionally energy stable, where the energy stabilitiesare proved rigorously. Various numerical tests are performed to show the accuracyand efficiency thereafter.