Efficient energy stable numerical schemes for Cahn–Hilliard equations with dynamical boundary conditions.

In this paper, we propose a unified framework for studying the Cahn–Hilliard equation with two distinct types of dynamic boundary conditions, namely, the Allen–Cahn and Cahn–Hilliard types. Using this unified framework, we develop a linear, second-order, and energy-stable scheme based on the multiple scalar auxiliary variables (MSAV) approach. We design efficient and decoupling algorithms for solving the corresponding linear system in which the unknown variables are intricately coupled both in the bulk and at the boundary. Several numerical experiments are shown to validate the proposed scheme, and to investigate the effect of different dynamical boundary conditions on the dynamics of phase evolution under different scenarios. [ABSTRACT FROM AUTHOR]