Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn–Hilliard Model

By Chuanjun Chen, Xiaofeng Yang. Computer Methods in Applied Mechanics and Engineering, 2019

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Abstract In this paper, we consider numerical approximations for solving the anisotropic Cahn–Hilliard model. We combine the Scalar Auxiliary Variable (SAV) approach with the stabilization technique to arrive at a novel Stabilized-SAV approach, where three linear stabilization terms, which are shown to be crucial to remove the oscillations caused by the anisotropic coefficient, are added to enhance the stability while keeping the required accuracy. The schemes are very easy-to-implement and fast in the sense that all nonlinear terms are treated in a semi-explicit way, and one only needs to solve three decoupled linear equations with constant coefficients at each time step. We further prove the unconditional energy stabilities rigorously and present numerous 2D and 3D numerical simulations to demonstrate the stability and accuracy.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/443a98a1a1fb01e70b4e43a790869f06931ff781