Phase-field model and its splitting numerical scheme for tissue growth
- Authors
- Jeong, Darae; Kim, Junseok
- Issue Date
- 7월-2017
- Publisher
- ELSEVIER
- Keywords
- Cahn-Hilliard equation; Tissue growth; Operator splitting method; Multigrid method
- Citation
- APPLIED NUMERICAL MATHEMATICS, v.117, pp.22 - 35
- Indexed
- SCIE
SCOPUS
- Journal Title
- APPLIED NUMERICAL MATHEMATICS
- Volume
- 117
- Start Page
- 22
- End Page
- 35
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/82955
- DOI
- 10.1016/j.apnum.2017.01.020
- ISSN
- 0168-9274
- Abstract
- We consider phase-field models and associated numerical methods for tissue growth. The model consists of the Cahn-Hilliard equation with a source term. In order to solve the equations accurately and efficiently, we propose a hybrid method based on an operator splitting method. First, we solve the contribution from the source term analytically and redistribute the increased mass around the tissue boundary position. Subsequently, we solve the Cahn-Hilliard equation using the nonlinearly gradient stable numerical scheme to make the interface transition profile smooth. We then perform various numerical experiments and find that there is a good agreement when these computational results are compared with analytic solutions. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.
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