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

On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential
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Year:    2019

Communications in Computational Physics, Vol. 25 (2019), Iss. 3 : pp. 703–728

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2017-0259

Communications in Computational Physics, Vol. 25 (2019), Iss. 3 : pp. 703–728

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Phase-field linear Cahn-Hilliard stability variable mobility Flory-Huggins.

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