An energy-stable method for a phase-field surfactant model

Zhijun Tan; Yuan Tian; Junxiang Yang; Yanyao Wu; Junseok Kim

doi:10.1016/j.ijmecsci.2022.107648

An energy-stable method for a phase-field surfactant model

Zhijun Tan, Yuan Tian, Junxiang Yang, Yanyao Wu, Junseok Kim

Department of Mathematics

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

2 Citations (Scopus)

Abstract

Two-phase systems with surfactants have extensive applications in scientific and industrial fields. In this paper, we consider a second-order time-accurate, highly efficient, and energy-stable scheme for a phase-field surfactant equation satisfying the energy boundedness. Because of the nonlinear and coupling terms in phase-field surfactant systems, it is not trivial to develop a totally decoupled and energy dissipation-preserving computational scheme. To address this challenge, we use an efficient variant of the scalar auxiliary variable (SAV) approach. The present method has the following merits: (i) The time-marching scheme is completely decoupled and the numerical implementation is efficient; (ii) the energy stability can be estimated in a straightforward manner; and (iii) various surfactant-laden dynamics can be well simulated. Various computational tests are conducted to validate the desired temporal accuracy, energy stability, and capability.

Original language	English
Article number	107648
Journal	International Journal of Mechanical Sciences
Volume	233
DOIs	https://doi.org/10.1016/j.ijmecsci.2022.107648
Publication status	Published - 2022 Nov 1

Keywords

Efficient algorithm
Energy dissipation
Novel SAV approach
Phase-field surfactant

ASJC Scopus subject areas

Civil and Structural Engineering
Materials Science(all)
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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10.1016/j.ijmecsci.2022.107648

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title = "An energy-stable method for a phase-field surfactant model",

abstract = "Two-phase systems with surfactants have extensive applications in scientific and industrial fields. In this paper, we consider a second-order time-accurate, highly efficient, and energy-stable scheme for a phase-field surfactant equation satisfying the energy boundedness. Because of the nonlinear and coupling terms in phase-field surfactant systems, it is not trivial to develop a totally decoupled and energy dissipation-preserving computational scheme. To address this challenge, we use an efficient variant of the scalar auxiliary variable (SAV) approach. The present method has the following merits: (i) The time-marching scheme is completely decoupled and the numerical implementation is efficient; (ii) the energy stability can be estimated in a straightforward manner; and (iii) various surfactant-laden dynamics can be well simulated. Various computational tests are conducted to validate the desired temporal accuracy, energy stability, and capability.",

keywords = "Efficient algorithm, Energy dissipation, Novel SAV approach, Phase-field surfactant",

author = "Zhijun Tan and Yuan Tian and Junxiang Yang and Yanyao Wu and Junseok Kim",

note = "Funding Information: The work of Z. Tan is supported by the National Nature Science Foundation of China ( 11971502 ), Guangdong Natural Science Foundation, China ( 2022A1515010426 ), Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University, China ( 2020B1212060032 ), and Key-Area Research and Development Program of Guangdong Province, China ( 2021B0101190003 ). J. Yang is supported by the China Postdoctoral Science Foundation (No. 2022M713639 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A2C1003844 ). The authors thank the reviewers for the constructive comments on the revision. Publisher Copyright: {\textcopyright} 2022 Elsevier Ltd",

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doi = "10.1016/j.ijmecsci.2022.107648",

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T1 - An energy-stable method for a phase-field surfactant model

AU - Tan, Zhijun

AU - Tian, Yuan

AU - Yang, Junxiang

AU - Wu, Yanyao

AU - Kim, Junseok

N1 - Funding Information: The work of Z. Tan is supported by the National Nature Science Foundation of China ( 11971502 ), Guangdong Natural Science Foundation, China ( 2022A1515010426 ), Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University, China ( 2020B1212060032 ), and Key-Area Research and Development Program of Guangdong Province, China ( 2021B0101190003 ). J. Yang is supported by the China Postdoctoral Science Foundation (No. 2022M713639 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A2C1003844 ). The authors thank the reviewers for the constructive comments on the revision. Publisher Copyright: © 2022 Elsevier Ltd

PY - 2022/11/1

Y1 - 2022/11/1

N2 - Two-phase systems with surfactants have extensive applications in scientific and industrial fields. In this paper, we consider a second-order time-accurate, highly efficient, and energy-stable scheme for a phase-field surfactant equation satisfying the energy boundedness. Because of the nonlinear and coupling terms in phase-field surfactant systems, it is not trivial to develop a totally decoupled and energy dissipation-preserving computational scheme. To address this challenge, we use an efficient variant of the scalar auxiliary variable (SAV) approach. The present method has the following merits: (i) The time-marching scheme is completely decoupled and the numerical implementation is efficient; (ii) the energy stability can be estimated in a straightforward manner; and (iii) various surfactant-laden dynamics can be well simulated. Various computational tests are conducted to validate the desired temporal accuracy, energy stability, and capability.

AB - Two-phase systems with surfactants have extensive applications in scientific and industrial fields. In this paper, we consider a second-order time-accurate, highly efficient, and energy-stable scheme for a phase-field surfactant equation satisfying the energy boundedness. Because of the nonlinear and coupling terms in phase-field surfactant systems, it is not trivial to develop a totally decoupled and energy dissipation-preserving computational scheme. To address this challenge, we use an efficient variant of the scalar auxiliary variable (SAV) approach. The present method has the following merits: (i) The time-marching scheme is completely decoupled and the numerical implementation is efficient; (ii) the energy stability can be estimated in a straightforward manner; and (iii) various surfactant-laden dynamics can be well simulated. Various computational tests are conducted to validate the desired temporal accuracy, energy stability, and capability.

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An energy-stable method for a phase-field surfactant model

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