Benchmark Problems for the Numerical Schemes of the Phase-Field Equations. (21st January 2022)

• Record Type: Journal Article
• Authors: Hwang, Youngjin; Lee, Chaeyoung; Kwak, Soobin; Choi, Yongho; Ham, Seokjun; Kang, Seungyoon; Yang, Junxiang; Kim, Junseok
• Other Names: Villatoro Francisco R. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2022(2022)
• Publication Date: 2022-01-21
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2022/2751592
• Languages: English
• ISSNs: 1026-0226

Abstract

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.