A multigrid solution for the Cahn-Hilliard equation on nonuniform grids
- Authors
- Choi, Yongho; Jeong, Darae; Kim, Junseok
- Issue Date
- 15-1월-2017
- Publisher
- ELSEVIER SCIENCE INC
- Keywords
- Cahn-Hilliard equation; Nonuniform grid; Finite difference method; Multigrid method
- Citation
- APPLIED MATHEMATICS AND COMPUTATION, v.293, pp.320 - 333
- Indexed
- SCIE
SCOPUS
- Journal Title
- APPLIED MATHEMATICS AND COMPUTATION
- Volume
- 293
- Start Page
- 320
- End Page
- 333
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/84913
- DOI
- 10.1016/j.amc.2016.08.026
- ISSN
- 0096-3003
- 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. (C) 2016 Elsevier Inc. All rights reserved.
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Collections - College of Science > Department of Mathematics > 1. Journal Articles
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