On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential

Abstract

In this paper, we consider numerical approximations for the fourth-order Cahn-Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential. One numerical challenge in solving such system is how to develop proper temporal discretization for nonlinear terms in order to preserve its energy stability at the time-discrete level. We overcome it by developing a set of first and second order time marching schemes based on a newly developed "Invariant Energy Quadratization" approach. Its novelty is producing linear schemes, by discretizing all nonlinear terms semi-explicitly. We further rigorously prove all proposed schemes are unconditionally energy stable. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy, and efficiency of the proposed schemes thereafter.