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Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model

Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model
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Year:    2020

Author:    Yuzhe Qin, Zhen Xu, Hui Zhang, Zhengru Zhang

Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1389–1414

Abstract

Here, we develop a first and a second order time stepping schemes for a binary fluid-surfactant phase field model by using the scalar auxiliary variable approach. The free energy contains a double-well potential, a nonlinear coupling entropy and a Flory-Huggins potential. The resulting coupled system consists of a Cahn-Hilliard type equation and a Wasserstein type equation which leads to a degenerate problem. By introducing only one scalar auxiliary variable, the system is transformed into an equivalent form so that the nonlinear terms can be treated semi-explicitly. Both the schemes are linear and decoupled, thus they can be solved efficiently. We further prove that these semi-discretized schemes in time are unconditionally energy stable. Some numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2019-0175

Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1389–1414

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Binary fluid-surfactant scalar auxiliary variable approach unconditional energy stability linear scheme decoupled.

Author Details

Yuzhe Qin

Zhen Xu

Hui Zhang

Zhengru Zhang

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