Volume 18, Issue 3
A Positivity-Preserving and Convergent Numerical Scheme for the Binary Fluid-Surfactant System

Yuzhe Qin, Cheng Wang & Zhengru Zhang

Int. J. Numer. Anal. Mod., 18 (2021), pp. 399-425.

Published online: 2021-03

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  • Abstract

In this paper, we develop a first order (in time) numerical scheme for the binary fluid surfactant phase field model. The free energy contains a double-well potential, a nonlinear coupling entropy and a Flory-Huggins potential. The resulting coupled system consists of two Cahn-Hilliard type equations. This system is solved numerically by finite difference spatial approximation, in combination with convex splitting temporal discretization. We prove the proposed scheme is unique solvable, positivity-preserving and unconditionally energy stable. In addition, an optimal rate convergence analysis is provided for the proposed numerical scheme, which will be the first such result for the binary fluid-surfactant system. Newton iteration is used to solve the discrete system. Some numerical experiments are performed to validate the accuracy and energy stability of the proposed scheme.

  • Keywords

Binary fluid-surfactant system, convex splitting, positivity-preserving, unconditional energy stability, Newton iteration

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-399, author = {Qin , Yuzhe and Wang , Cheng and Zhang , Zhengru}, title = {A Positivity-Preserving and Convergent Numerical Scheme for the Binary Fluid-Surfactant System}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {3}, pages = {399--425}, abstract = {

In this paper, we develop a first order (in time) numerical scheme for the binary fluid surfactant phase field model. The free energy contains a double-well potential, a nonlinear coupling entropy and a Flory-Huggins potential. The resulting coupled system consists of two Cahn-Hilliard type equations. This system is solved numerically by finite difference spatial approximation, in combination with convex splitting temporal discretization. We prove the proposed scheme is unique solvable, positivity-preserving and unconditionally energy stable. In addition, an optimal rate convergence analysis is provided for the proposed numerical scheme, which will be the first such result for the binary fluid-surfactant system. Newton iteration is used to solve the discrete system. Some numerical experiments are performed to validate the accuracy and energy stability of the proposed scheme.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18727.html} }
TY - JOUR T1 - A Positivity-Preserving and Convergent Numerical Scheme for the Binary Fluid-Surfactant System AU - Qin , Yuzhe AU - Wang , Cheng AU - Zhang , Zhengru JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 399 EP - 425 PY - 2021 DA - 2021/03 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18727.html KW - Binary fluid-surfactant system, convex splitting, positivity-preserving, unconditional energy stability, Newton iteration AB -

In this paper, we develop a first order (in time) numerical scheme for the binary fluid surfactant phase field model. The free energy contains a double-well potential, a nonlinear coupling entropy and a Flory-Huggins potential. The resulting coupled system consists of two Cahn-Hilliard type equations. This system is solved numerically by finite difference spatial approximation, in combination with convex splitting temporal discretization. We prove the proposed scheme is unique solvable, positivity-preserving and unconditionally energy stable. In addition, an optimal rate convergence analysis is provided for the proposed numerical scheme, which will be the first such result for the binary fluid-surfactant system. Newton iteration is used to solve the discrete system. Some numerical experiments are performed to validate the accuracy and energy stability of the proposed scheme.

​Yuzhe Qin, Cheng Wang & Zhengru Zhang. (2021). A Positivity-Preserving and Convergent Numerical Scheme for the Binary Fluid-Surfactant System. International Journal of Numerical Analysis and Modeling. 18 (3). 399-425. doi:
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