Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization

JOURNAL OF COMPUTATIONAL PHYSICS

卷:365

Article

Chen, Ying¹  Lowengrub, John²  Shen, Jie³  Wang, Cheng⁴  Wise, Steven⁵ 

[1] Duke Univ, Dept Math, Durham, NC 27708 USA

[2] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[3] Purdue Univ, Dept Math, W Lafayette, IN 47906 USA

[4] Univ Massachusetts, Dept Math, N Dartmouth, MA 02747 USA

[5] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

关键词: Phase-field;    Cahn-Hilliard;    Anisotropy;    Willmore regularization;    Multigrid method;    Energy stable;   

DOI  :  10.1016/j.jcp.2018.03.024

来源: Elsevier

【 摘 要 】

We develop efficient energy stable numerical methods for solving isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. The scheme, which involves adaptive mesh refinement and a nonlinear multigrid finite difference method, is constructed based on a convex splitting approach. We prove that, for the isotropic Cahn-Hilliard system with the Willmore regularization, the total free energy of the system is non-increasing for any time step and mesh sizes. A straightforward modification of the scheme is then used to solve the regularized strongly anisotropic Cahn-Hilliard system, and it is numerically verified that the discrete energy of the anisotropic system is also non-increasing, and can be efficiently solved by using the modified stable method. We present numerical results in both two and three dimensions that are in good agreement with those in earlier work on the topics. Numerical simulations are presented to demonstrate the accuracy and efficiency of the proposed methods. (C) 2018 Published by Elsevier Inc.

【 授权许可】

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