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.