An integral equation method for the Cahn-Hilliard equation inthe wetting problem

JOURNAL OF COMPUTATIONAL PHYSICS

卷:419

Article

Wei, Xiaoyu²  Jiang, Shidong¹  Klockner, Andreas²  Wang, Xiao-Ping³ 

[1] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA

[2] Univ Illinois, Dept Comp Sci, Urbana, IL 61801 USA

[3] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Clear Water Bay, Hong Kong, Peoples R China

关键词: Integral equation method;    Cahn-Hilliard equation;    Young's angle;    Convex splitting;    Volume potential;    Second-kind integral equation;   

DOI  :  10.1016/j.jcp.2020.109521

来源: Elsevier

【 摘 要 】

We present an integral equation approach to solving the Cahn-Hilliard equation equipped with boundary conditions that model solid surfaces with prescribed Young's angles. The discretization of the system in time using convex splitting leads to a modified biharmonic equation at each time step. To solve it, we split the solution into a volume potential computed with free space kernels, plus the solution to a second kind integral equation (SKIE). The volume potential is evaluated with the help of a box-based volume-FMM method. For non-box domains, the source density is extended by solving a biharmonic Dirichlet problem. The near-singular boundary integrals are computed using quadrature by expansion (QBX) with FMM acceleration. Our method has linear complexity in the number of surface/volume degrees of freedom and can achieve high order convergence in space with adaptive refinement to manage error from function extension. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free