Benchmark Problems for the Numerical Discretization of the Cahn–Hilliard Equation with a Source Term. (6th December 2021)

• Record Type: Journal Article
• Authors: Yoon, Sungha; Lee, Hyun Geun; Li, Yibao; Lee, Chaeyoung; Park, Jintae; Kim, Sangkwon; Kim, Hyundong; Kim, Junseok
• Other Names: Karachalios Nikos I. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2021(2021)
• Publication Date: 2021-12-06
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2021/1290895
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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.