A conservative finite difference scheme for the N-component Cahn–Hilliard system on curved surfaces in 3D

Junxiang Yang, Yibao Li, Chaeyoung Lee, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticle

Abstract

This paper presents a conservative finite difference scheme for solving the N-component Cahn–Hilliard (CH) system on curved surfaces in three-dimensional (3D) space. Inspired by the closest point method (Macdonald and Ruuth, SIAM J Sci Comput 31(6):4330–4350, 2019), we use the standard seven-point finite difference discretization for the Laplacian operator instead of the Laplacian–Beltrami operator. We only need to independently solve (N- 1) CH equations in a narrow band domain around the surface because the solution for the Nth component can be obtained directly. The N-component CH system is discretized using an unconditionally stable nonlinear splitting numerical scheme, and it is solved by using a Jacobi-type iteration. Several numerical tests are performed to demonstrate the capability of the proposed numerical scheme. The proposed multicomponent model can be simply modified to simulate phase separation in a complex domain on 3D surfaces.

Original languageEnglish
Pages (from-to)149-166
Number of pages18
JournalJournal of Engineering Mathematics
Volume119
Issue number1
DOIs
Publication statusPublished - 2019 Dec 1

Keywords

  • Closest point method
  • Conservative scheme
  • N-component Cahn–Hilliard equation
  • Narrow band domain

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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