A Positivity-Preserving and Convergent Numerical Scheme for the Binary Fluid-Surfactant System

A Positivity-Preserving and Convergent Numerical Scheme for the Binary Fluid-Surfactant System

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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

Author Details

Yuzhe Qin

Cheng Wang

Zhengru Zhang