Journal
COMPUTER PHYSICS COMMUNICATIONS
Volume 238, Issue -, Pages 36-49Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cpc.2018.12.019
Keywords
Anisotropy; Phase-field; Cahn-Hilliard; Energy stability; IEQ method; Second-order
Funding
- China Scholarship Council [201706040140]
- National Science Foundation (NSF) [DMS-1720212, 1818783, NSFC-11471046, NSFC-11571045, NSFC-11771138, NSFC-11171104, NSFC-91430107]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1818783] Funding Source: National Science Foundation
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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. (C) 2018 Elsevier B.V. All rights reserved.
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