Year: 2021
Author: Yuzhe Qin, Cheng Wang, Zhengru Zhang
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-18727
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 3 : pp. 399–425
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Binary fluid-surfactant system convex splitting positivity-preserving unconditional energy stability Newton iteration