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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 = {Yuzhe and Qin and and 14636 and and Yuzhe Qin and Cheng and Wang and and 14637 and and Cheng Wang and Zhengru and Zhang and and 14638 and and Zhengru Zhang}, 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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