In this paper, we consider numerical approximations for the anisotropic Cahn–Hilliard equation. We develop two linear and second-order schemes that combine the IEQ approach with the stabilization technique, where several extra linear stabilization terms are added in and they can be shown to be crucial to suppress the non-physical spatial oscillations caused by the strong anisotropy. We show the well-posedness of the resulting linear systems and further prove their corresponding unconditional energy stabilities rigorously. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy, and efficiency of the proposed schemes.
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Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn–Hilliard Model
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.
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- Award ID(s):
- 1720212
- NSF-PAR ID:
- 10100286
- Date Published:
- Journal Name:
- Computer methods in applied mechanics and engineering
- ISSN:
- 1879-2138
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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