A benchmark problem for the two- and three-dimensional Cahn-Hilliard equations
- Authors
- Jeong, Darae; Choi, Yongho; Kim, Junseok
- Issue Date
- 8월-2018
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Cahn-Hilliard equation; Finite difference method; Multigrid method; Benchmark problem
- Citation
- COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v.61, pp.149 - 159
- Indexed
- SCIE
SCOPUS
- Journal Title
- COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
- Volume
- 61
- Start Page
- 149
- End Page
- 159
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/74220
- DOI
- 10.1016/j.cnsns.2018.02.006
- ISSN
- 1007-5704
- Abstract
- This paper proposes a benchmark problem for the two-and three-dimensional Cahn-Hilliard (CH) equations, which describe the process of phase separation. The CH equation is highly nonlinear and an analytical solution does not exist except trivial solutions. Therefore, we have to approximate the CH equation numerically. To test the accuracy of a numerical scheme, we have to resort to convergence tests, which consist of consecutive relative errors or a very fine solution from the numerical scheme. For a fair convergence test, we provide benchmark problems which are of the shrinking annulus and spherical shell type. We show numerical results by using the explicit Euler's scheme with a very fine time step size and also present a comparison test with Eyre's convex splitting schemes. (C) 2018 Elsevier B.V. All rights reserved.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Science > Department of Mathematics > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholar.korea.ac.kr/handle/2021.sw.korea/74220)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.