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Efficient, non-iterative, and decoupled numerical scheme for a new modified binary phase-field surfactant system

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Abstract

We consider in this paper numerical approximations of a Cahn-Hilliard binary phase-field fluid-surfactant model. By adding a quartic form of the gradient potential, we first modify the commonly used total free energy into a form which is bounded from below and establish the energy law for the new system. Then we develop a stabilized-SAV scheme that combines the SAV approach with the stabilization technique, where a crucial linear stabilization term is added to enhance the stability thus allowing large time steps. With many desired properties such as a second-order in time, totally decoupled, linear, and non-iterative, this scheme is unconditionally energy stable and requires solving only four decoupled and linear biharmonic equations with constant coefficients at each time step. We further prove the energy stability and present numerous 2D and 3D numerical simulations to demonstrate the accuracy and stability of the developed scheme

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Funding

C. Xu is partially supported by NSFC-61872429. C. Chen was partially supported by Natural Science Foundation of China (11771375 and 11571297). X. Yang was partially supported by National Science Foundation with grant numbers DMS (1720212 and 1818783). X. Yang is partially supported by NSF DMS-1720212 and DMS-1818783.

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Authors and Affiliations

  1. Institute of Intelligent Computing Science, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Chen Xu

  2. School of Mathematics and Information Sciences, Yantai University, Yantai, 264005, China

    Chuanjun Chen

  3. Department of Mathematics, University of South Carolina, Columbia, South Carolina, 29208, USA

    Xiaofeng Yang

Authors
  1. Chen Xu
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  2. Chuanjun Chen
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  3. Xiaofeng Yang
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Correspondence to Chuanjun Chen.

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Xu, C., Chen, C. & Yang, X. Efficient, non-iterative, and decoupled numerical scheme for a new modified binary phase-field surfactant system. Numer Algor 86, 863–885 (2021). https://doi.org/10.1007/s11075-020-00915-8

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