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Conservative Allen–Cahn equation with a nonstandard variable mobility

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea

    Junxiang Yang, Chaeyoung Lee & Junseok Kim

  2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Yibao Li

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  1. Junxiang Yang
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  2. Yibao Li
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Correspondence to Junseok Kim.

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Yang, J., Li, Y., Lee, C. et al. Conservative Allen–Cahn equation with a nonstandard variable mobility. Acta Mech 231, 561–576 (2020). https://doi.org/10.1007/s00707-019-02548-y

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  • DOI: https://doi.org/10.1007/s00707-019-02548-y

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