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Volume 28, Issue 4
Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model

Yuzhe Qin, Zhen Xu, Hui Zhang & Zhengru Zhang

DOI: 10.4208/cicp.OA-2019-0175

Commun. Comput. Phys., 28 (2020), pp. 1389-1414.

Published online: 2020-08

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35K35, 35K55, 65M12, 65M22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-1389, author = {Qin , YuzheXu , ZhenZhang , Hui and Zhang , Zhengru}, title = {Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0175}, url = {http://global-sci.org/intro/article_detail/cicp/18105.html} }
TY - JOUR T1 - Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model AU - Qin , Yuzhe AU - Xu , Zhen AU - Zhang , Hui AU - Zhang , Zhengru JO - Communications in Computational Physics VL - 4 SP - 1389 EP - 1414 PY - 2020 DA - 2020/08 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2019-0175 UR - https://global-sci.org/intro/article_detail/cicp/18105.html KW - Binary fluid-surfactant, scalar auxiliary variable approach, unconditional energy stability, linear scheme, decoupled. AB -

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.

Qin , YuzheXu , ZhenZhang , Hui and Zhang , Zhengru. (2020). Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model. Communications in Computational Physics. 28 (4). 1389-1414. doi:10.4208/cicp.OA-2019-0175
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