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

Youngjin Hwang, Chaeyoung Lee, Soobin Kwak, Yongho Choi, Seokjun Ham, Seungyoon Kang, Junxiang Yang, Junseok Kim

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number2751592
JournalDiscrete Dynamics in Nature and Society
Volume2022
DOIs
Publication statusPublished - 2022

ASJC Scopus subject areas

  • Modelling and Simulation

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