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

Yongho Choi, Darae Jeong and Junseok Kim

Applied Mathematics and Computation, 2017, vol. 293, issue C, 320-333

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.

Keywords: Cahn–Hilliard equation; Nonuniform grid; Finite difference method; Multigrid method (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:293:y:2017:i:c:p:320-333

DOI: 10.1016/j.amc.2016.08.026

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