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

Author

Listed:
  • Sungha Yoon
  • Hyun Geun Lee
  • Yibao Li
  • Chaeyoung Lee
  • Jintae Park
  • Sangkwon Kim
  • Hyundong Kim
  • Junseok Kim
  • Nikos I. Karachalios

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.

Suggested Citation

  • Sungha Yoon & Hyun Geun Lee & Yibao Li & Chaeyoung Lee & Jintae Park & Sangkwon Kim & Hyundong Kim & Junseok Kim & Nikos I. Karachalios, 2021. "Benchmark Problems for the Numerical Discretization of the Cahn–Hilliard Equation with a Source Term," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-11, December.
    • Handle: RePEc:hin:jnddns:1290895
    DOI: 10.1155/2021/1290895
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    Cited by:

    1. Yang, Junxiang & Lee, Dongsun & Kwak, Soobin & Ham, Seokjun & Kim, Junseok, 2024. "The Allen–Cahn model with a time-dependent parameter for motion by mean curvature up to the singularity," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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