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

Soobin Kwak, Junxiang Yang, Junseok Kim

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number107838
JournalApplied Mathematics Letters
Volume126
DOIs
Publication statusPublished - 2022 Apr

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

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