Conservative Allen–Cahn equation with a nonstandard variable mobility

Junxiang Yang; Yibao Li; Chaeyoung Lee; Junseok Kim

doi:10.1007/s00707-019-02548-y

Conservative Allen–Cahn equation with a nonstandard variable mobility

Junxiang Yang, Yibao Li, Chaeyoung Lee, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	561-576
Number of pages	16
Journal	Acta Mechanica
Volume	231
Issue number	2
DOIs	https://doi.org/10.1007/s00707-019-02548-y
Publication status	Published - 2020 Feb 1

Bibliographical note

Funding Information:
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).

Publisher Copyright:
© 2019, Springer-Verlag GmbH Austria, part of Springer Nature.

ASJC Scopus subject areas

Computational Mechanics
Mechanical Engineering

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10.1007/s00707-019-02548-y

Cite this

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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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Conservative Allen–Cahn equation with a nonstandard variable mobility

Abstract

Bibliographical note

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