A second-order energy stable numerical scheme of the modified Cahn–Hilliard equation for simulating wetting phenomena

In this paper, we design a second-order unconditional energy stable numerical scheme for the modified Cahn–Hilliard phase field model simulating wetting phenomenon. We use the scalar auxiliary variable (SAV) method to transform the Cahn–Hilliard equation into an equivalent form, use second-order backward difference formula (BDF2) for time discretization and finite element method (FEM) for space discretization. A relaxation technique is employed to correct the numerical errors of the scalar auxiliary variable. The scheme is proved to be unconditionally energy stable. We perform several numerical experiments for wetting phenomena on flat, curved and rough substrates, demonstrating the capability of our proposed numerical scheme. At the same time, we also combine our numerical scheme with an adaptive time stepping strategy for acceleration.