Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:343

Article

Yang, Xiaofeng¹  Zhao, Jia²  He, Xiaoming^3,4 

[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

[2] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

[3] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA

[4] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 610054, Sichuan, Peoples R China

关键词: Phase-field;    Linear;    Cahn-Hilliard;    Stability;    Variable mobility;    Flory-Huggins;   

DOI  :  10.1016/j.cam.2018.04.027

来源: Elsevier

【 摘 要 】

In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system numerically is how to develop high order temporal discretization for the hyperbolic and nonlinear terms, allowing large time-marching step, while preserving the energy stability, i.e. the energy dissipative structure at the time-discrete level. We resolve this issue by developing two second-order time-marching schemes using the recently developed Invariant Energy Quadratization approach where all nonlinear terms are discretized semi-explicitly. In each time step, one only needs to solve a symmetric positive definite (SPD) linear system. All the proposed schemes are rigorously proven to be unconditionally energy stable, and the second-order convergence in time has been verified by time step refinement tests numerically. 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.

【 授权许可】

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