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Journal of Scientific Computing

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01-02-2020

Stabilized Energy Factorization Approach for Allen–Cahn Equation with Logarithmic Flory–Huggins Potential

Authors: Xiuhua Wang, Jisheng Kou, Jianchao Cai

Published in: Journal of Scientific Computing | Issue 2/2020

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Abstract

The Allen–Cahn equation is one of fundamental equations of phase-field models, while the logarithmic Flory–Huggins potential is one of the most useful energy potentials in various phase-field models. In this paper, we consider numerical schemes for solving the Allen–Cahn equation with logarithmic Flory–Huggins potential. The main challenge is how to design efficient numerical schemes that preserve the maximum principle and energy dissipation law due to the strong nonlinearity of the energy potential function. We propose a novel energy factorization approach with the stabilization technique, which is called stabilized energy factorization approach, to deal with the Flory–Huggins potential. One advantage of the proposed approach is that all nonlinear terms can be treated semi-implicitly and the resultant numerical scheme is purely linear and easy to implement. Moreover, the discrete maximum principle and unconditional energy stability of the proposed scheme are rigorously proved using the discrete variational principle. Numerical results are presented to demonstrate the stability and effectiveness of the proposed scheme.

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Title: Stabilized Energy Factorization Approach for Allen–Cahn Equation with Logarithmic Flory–Huggins Potential
Authors: Xiuhua Wang
Jisheng Kou
Jianchao Cai
Publication date: 01-02-2020
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2020
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01127-x

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