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.
| Original language | English |
|---|---|
| Pages (from-to) | 22-35 |
| Number of pages | 14 |
| Journal | Applied Numerical Mathematics |
| Volume | 117 |
| DOIs | |
| Publication status | Published - 2017 Jul 1 |
Bibliographical note
Funding Information:The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper. The first author (D. Jeong) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2014R1A6A3A01009812). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683).
Publisher Copyright:
© 2017 IMACS
Keywords
- Cahn–Hilliard equation
- Multigrid method
- Operator splitting method
- Tissue growth
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics