Volume 25, Issue 3
On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential

Xiaofeng Yang and Jia Zhao

10.4208/cicp.OA-2017-0259

Commun. Comput. Phys., 25 (2019), pp. 703-728.

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  • 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.

  • History

Published online: 2018-11

  • AMS Subject Headings

65N12, 65P40, 65Z05

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