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An Adaptive Time-Stepping Method for the Binary Fluid-Surfactant Phase Field Model on Evolving Surfaces

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Abstract

In this paper, the binary fluid-surfactant phase field model on evolving surfaces is presented and numerically studied for interfacial sciences. Based on the evolving surface finite element method, the first-order and second-order standard semi-implicit schemes are shown and analyzed to be conditionally stable. The energy dissipation law of the binary fluid-surfactant phase field model does not hold for evolving surfaces with arbitrary surface velocities which can be viewed as an action of external force. Therefore, this paper is dedicated to addressing the difficulties of conditional stability and numerical stiffness caused by the small interfacial parameters instead of energy stability. The first-order and second-order stabilizing approaches are employed to improve the stabilities of semi-implicit schemes. For the efficiency of long time simulation, an adaptive time-stepping technique considering energy evolution and surface velocity is developed. The effectiveness of the proposed stabilizing and adaptive time-stepping approaches is verified by numerical experiments. Various numerical simulations are performed to demonstrate the effectiveness and efficiency of the proposed method, and numerically investigate the behavior of the binary fluid-surfactant on evolving surfaces.

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Data availability

No data was used for the research described in the article. The codes generated during the study are all available on request from the corresponding author Xufeng Xiao.

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Acknowledgements

The authors would like to thank the editors and referees for their valuable comments and suggestions which helped us to improve the results of this paper.

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  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Shijie Huang, Xufeng Xiao & Xinlong Feng

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  1. Shijie Huang
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  2. Xufeng Xiao
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Correspondence to Xufeng Xiao.

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This work is supported by the NSF of China (No. 12001466, No. U19A2079 and No. 11671345), the scientific research plan of universities in Xinjiang (No. XJEDU2020Y001 and No. XJEDU2020I001), and the Research Fund from Key Laboratory of Xinjiang Province (No. 2020D04002).

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Huang, S., Xiao, X. & Feng, X. An Adaptive Time-Stepping Method for the Binary Fluid-Surfactant Phase Field Model on Evolving Surfaces. J Sci Comput 95, 29 (2023). https://doi.org/10.1007/s10915-023-02150-4

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  • DOI: https://doi.org/10.1007/s10915-023-02150-4

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