@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} }