TY - JOUR
T1 - Benchmark Problems for the Numerical Discretization of the Cahn-Hilliard Equation with a Source Term
AU - Yoon, Sungha
AU - Lee, Hyun Geun
AU - Li, Yibao
AU - Lee, Chaeyoung
AU - Park, Jintae
AU - Kim, Sangkwon
AU - Kim, Hyundong
AU - Kim, Junseok
N1 - Publisher Copyright:
© 2021 Sungha Yoon et al.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85122308263&partnerID=8YFLogxK
U2 - 10.1155/2021/1290895
DO - 10.1155/2021/1290895
M3 - Article
AN - SCOPUS:85122308263
SN - 1026-0226
VL - 2021
JO - Discrete Dynamics in Nature and Society
JF - Discrete Dynamics in Nature and Society
M1 - 1290895
ER -