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Benchmark Problems for the Numerical Schemes of the Phase-Field Equations

Author

Listed:
  • Youngjin Hwang
  • Chaeyoung Lee
  • Soobin Kwak
  • Yongho Choi
  • Seokjun Ham
  • Seungyoon Kang
  • Junxiang Yang
  • Junseok Kim
  • Francisco R. Villatoro

Abstract

In this study, we present benchmark problems for the numerical methods of the phase-field equations. To find appropriate benchmark problems, we first perform a linear stability analysis and then take a growth mode solution as the benchmark problem, which is closely related to the dynamics of the original governing equations. As concrete examples, we perform convergence tests of the numerical methods of the Allen–Cahn (AC) and Cahn–Hilliard (CH) equations using the proposed benchmark problems. The one- and two-dimensional computational experiments confirm the accuracy and efficiency of the proposed scheme as the benchmark problems.

Suggested Citation

  • Youngjin Hwang & Chaeyoung Lee & Soobin Kwak & Yongho Choi & Seokjun Ham & Seungyoon Kang & Junxiang Yang & Junseok Kim & Francisco R. Villatoro, 2022. "Benchmark Problems for the Numerical Schemes of the Phase-Field Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-10, January.
    • Handle: RePEc:hin:jnddns:2751592
    DOI: 10.1155/2022/2751592
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