Numerical Simulation for Moving Contact Line with Continuous Finite Element Schemes (Communications in Computational Physics, 2018)
In this paper, we compute a phase field (diffuse interface) model of Cahn-Hilliardtype for moving contact line problems governing the motion of isothermalmultiphase incompressible fluids. The generalized Navier boundary condition proposedby Qian et al. [1] is adopted here. We discretize model equations using a continuousfinite element method in space and a modified midpoint scheme in time. Weapply a penalty formulation to the continuity equation which may increase the stabilityin the pressure variable. Two kinds of immiscible fluids in a pipe and droplet displacementwith a moving contact line under the effect of pressure driven shear floware studied using a relatively coarse grid. We also derive the discrete energy law forthe droplet displacement case, which is slightly different due to the boundary conditions.The accuracy and stability of the scheme are validated by examples, results andestimate order.