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

doi:10.1155/2022/2751592

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 language	English
Article number	2751592
Journal	Discrete Dynamics in Nature and Society
Volume	2022
DOIs	https://doi.org/10.1155/2022/2751592
Publication status	Published - 2022

ASJC Scopus subject areas

Modelling and Simulation

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10.1155/2022/2751592

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title = "Benchmark Problems for the Numerical Schemes of the Phase-Field Equations",

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.",

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

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AU - Hwang, Youngjin

AU - Lee, Chaeyoung

AU - Kwak, Soobin

AU - Choi, Yongho

AU - Ham, Seokjun

AU - Kang, Seungyoon

AU - Yang, Junxiang

AU - Kim, Junseok

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

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VL - 2022

JO - Discrete Dynamics in Nature and Society

JF - Discrete Dynamics in Nature and Society

M1 - 2751592

ER -

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

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