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

Soobin Kwak, Junxiang Yang, Junseok Kim

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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 languageEnglish
Article number107838
JournalApplied Mathematics Letters
Publication statusPublished - 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


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

ASJC Scopus subject areas

  • Applied Mathematics


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