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 - <p style="text-align: justify;">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.<br/></p>