Efficient, adaptive energy stable schemes for the incompressible Cahn Hilliard Navier Stokes phase field models
In this paper we develop a fully adaptive energy stable scheme for Cahn Hilliard Navier Stokes system, which is a phase field model for two phase incompressible flows, consisting a Cahn Hilliard type diffusion equation and a Navier Stokes equation. This scheme, which is decoupled and unconditionally energy stable based on stabilization, involves adaptive mesh, adaptive time and a nonlinear multigrid finite difference method. Numerical experiments are carried out to validate the scheme for problems with matched density and non matched density, and also demonstrate that CPU time can be significantly reduced with our adaptive approach.
J. Comput. Phys.