A multigrid solution for the Cahn–Hilliard equation on nonuniform grids

Yongho Choi, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We present a nonlinear multigrid method to solve the Cahn–Hilliard (CH) equation on nonuniform grids. The CH equation was originally proposed as a mathematical model to describe phase separation phenomena after the quenching of binary alloys. The model has the characteristics of thin diffusive interfaces. To resolve the sharp interfacial transition, we need a very fine grid, which is computationally expensive. To reduce the cost, we can use a fine grid around the interfacial transition region and a relatively coarser grid in the bulk region. The CH equation is discretized by a conservative finite difference scheme in space and an unconditionally gradient stable type scheme in time. We use a conservative restriction in the nonlinear multigrid method to conserve the total mass in the coarser grid levels. Various numerical results on one-, two-, and three-dimensional spaces are presented to demonstrate the accuracy and effectiveness of the nonuniform grids for the CH equation.

Original languageEnglish
Pages (from-to)320-333
Number of pages14
JournalApplied Mathematics and Computation
Volume293
DOIs
Publication statusPublished - 2017 Jan 15

Keywords

  • Cahn–Hilliard equation
  • Finite difference method
  • Multigrid method
  • Nonuniform grid

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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