TY - JOUR
T1 - A conservative Allen–Cahn equation with a curvature-dependent Lagrange multiplier
AU - Kwak, Soobin
AU - Yang, Junxiang
AU - Kim, Junseok
N1 - 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
PY - 2022/4
Y1 - 2022/4
N2 - 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.
AB - 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.
KW - Conservative Allen–Cahn equation
KW - Fourier-spectral method
KW - Structure-preserving model
UR - http://www.scopus.com/inward/record.url?scp=85120902864&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2021.107838
DO - 10.1016/j.aml.2021.107838
M3 - Article
AN - SCOPUS:85120902864
SN - 0893-9659
VL - 126
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
M1 - 107838
ER -