A conservative Allen–Cahn equation with a curvature-dependent Lagrange multiplier

Soobin Kwak; Junxiang Yang; Junseok Kim

doi:10.1016/j.aml.2021.107838

A conservative Allen–Cahn equation with a curvature-dependent Lagrange multiplier

Soobin Kwak, Junxiang Yang, Junseok Kim

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

13 Citations (Scopus)

Abstract

In the present study, we propose a novel conservative Allen–Cahn (CAC) equation with a curvature-dependent Lagrange multiplier. The proposed CAC equation has a superior structure-preserving property. Unlike the conventional CAC equations which have motion by mean curvature with area or volume constraint, the proposed model has minimum dynamics of motion by mean curvature and only has smoothing property of interface transition layer. Therefore, it can be utilized as a building block equation for modeling conservative phase-field applications such as two-phase fluid flows. Several computational tests are conducted to confirm the superior performance of the proposed CAC equation in terms of structure-preserving property.

Original language	English
Article number	107838
Journal	Applied Mathematics Letters
Volume	126
DOIs	https://doi.org/10.1016/j.aml.2021.107838
Publication status	Published - 2022 Apr

Bibliographical note

Funding Information:
The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1A2C1003053 ). The authors would like to thank the reviewers for their constructive comments and suggestions.

Publisher Copyright:
© 2021 Elsevier Ltd

Keywords

Conservative Allen–Cahn equation
Fourier-spectral method
Structure-preserving model

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2021.107838

Cite this

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abstract = "In the present study, we propose a novel conservative Allen–Cahn (CAC) equation with a curvature-dependent Lagrange multiplier. The proposed CAC equation has a superior structure-preserving property. Unlike the conventional CAC equations which have motion by mean curvature with area or volume constraint, the proposed model has minimum dynamics of motion by mean curvature and only has smoothing property of interface transition layer. Therefore, it can be utilized as a building block equation for modeling conservative phase-field applications such as two-phase fluid flows. Several computational tests are conducted to confirm the superior performance of the proposed CAC equation in terms of structure-preserving property.",

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A conservative Allen–Cahn equation with a curvature-dependent Lagrange multiplier

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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