Conservative Allen–Cahn equation with a nonstandard variable mobility

  • Junxiang Yang
  • Yibao Li
  • Chaeyoung Lee
  • Junseok KimEmail author
Original Paper


In this article, we present the conservative Allen–Cahn equation with a nonstandard variable mobility. Unlike the classical variable mobility, the proposed nonstandard variable mobility has small value at the interface and large value away from the interface. As benchmark tests, we perform temporal evolutions of two droplets without velocity field, 2D droplet deformation under a simple shear flow, 2D droplet deformation under a swirling flow, and 3D droplet deformation under a shear flow. The numerical results of the proposed method demonstrate a remarkable accuracy in preserving interfaces. Moreover, the proposed method not only captures interface location but also maintains uniform interface transition layer thickness.



Y. B. Li is supported by National Natural Science Foundation of China (Nos. 11601416, 11631012). 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).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Junxiang Yang
    • 1
  • Yibao Li
    • 2
  • Chaeyoung Lee
    • 1
  • Junseok Kim
    • 1
    Email author
  1. 1.Department of MathematicsKorea UniversitySeoulRepublic of Korea
  2. 2.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina

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