On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential (Communications in Computational Physics, 2018)
In this paper, we consider numerical approximations for the fourth-orderCahn-Hilliard equation with the concentration-dependent mobility and the logarithmicFlory-Huggins bulk potential. One numerical challenge in solving such systemis how to develop proper temporal discretization for nonlinear terms in order to preserveits energy stability at the time-discrete level. We overcome it by developing aset of first and second order time marching schemes based on a newly developed "InvariantEnergy Quadratization" approach. Its novelty is producing linear schemes,by discretizing all nonlinear terms semi-explicitly. We further rigorously prove allproposed schemes are unconditionally energy stable. Various 2D and 3D numericalsimulations are presented to demonstrate the stability, accuracy, and efficiency of theproposed schemes thereafter.
Keywords: Phase-field; linear; Cahn-Hilliard; stability; variable mobility; Flory-Huggins.