Benchmark Problems for the Numerical Discretization of the Cahn–Hilliard Equation with a Source Term

In this paper, we present benchmark problems for the numerical discretization of the Cahn–Hilliard equation with a source term. If the source term includes an isotropic growth term, then initially circular and spherical shapes should grow with their original shapes. However, there is numerical aniso...

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Bibliographic Details
Published inDiscrete dynamics in nature and society Vol. 2021; pp. 1 - 11
Main Authors Yoon, Sungha, Lee, Hyun Geun, Li, Yibao, Lee, Chaeyoung, Park, Jintae, Kim, Sangkwon, Kim, Hyundong, Kim, Junseok
Format Journal Article
LanguageEnglish
Published New York Hindawi 06.12.2021
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Anisotropy
Benchmarks
Discretization
Growth models
Laplace transforms
Simulation
New York
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Summary:In this paper, we present benchmark problems for the numerical discretization of the Cahn–Hilliard equation with a source term. If the source term includes an isotropic growth term, then initially circular and spherical shapes should grow with their original shapes. However, there is numerical anisotropic error and this error results in anisotropic evolutions. Therefore, it is essential to use isotropic space discretization in the simulation of growth phenomenon such as tumor growth. To test numerical discretization, we present two benchmark problems: one is the growth of a disk or a sphere and the other is the growth of a rotated ellipse or a rotated ellipsoid. The computational results show that the standard discrete Laplace operator has severe grid orientation dependence. However, the isotropic discrete Laplace operator generates good results.
ISSN:1026-0226
1607-887X
DOI:10.1155/2021/1290895