Decoupled, Energy Stable Scheme for Hydrodynamic Allen-Cahn Phase Field Moving Contact Line Model (Journal of Computational Mathematics, 2018)
In this paper, we present an efficient energy stable scheme to solve a phase field modelincorporating contact line condition. Instead of the usually used Cahn-Hilliard type phaseequation, we adopt the Allen-Cahn type phase field model with the static contact lineboundary condition that coupled with incompressible Navier-Stokes equations with Navierboundary condition. The projection method is used to deal with the Navier-Stokes equationsand an auxiliary function is introduced for the non-convex Ginzburg-Landau bulkpotential. We show that the scheme is linear, decoupled and energy stable. Moreover, weprove that fully discrete scheme is also energy stable. An efficient finite element spatialdiscretization method is implemented to verify the accuracy and efficiency of proposedschemes. Numerical results show that the proposed scheme is very efficient and accurate.