Numerical Approximations for the Hydrodynamics Coupled Binary Surfactant Phase Field Model: Second-Order, Linear, Unconditionally Energy Stable Schemes

Abstract

In this paper, we consider numerical approximations of a binary fluid-surfactant phase-field model coupled with the fluid flow, in which the system consists of the incompressible Navier-Stokes equations and two Cahn-Hilliard type equations. We develop two linear and second order time marching schemes for solving this system by combining the "Invariant Energy Quadratization" approach for the nonlinear potentials, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective terms. We prove the well-posedness of the linear system and its unconditional energy stability rigorously. Various 2D and 3D numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Cahn-Hilliard; Energy stability; fluid-surfactant; Navier-Stokes; Phase-field; Second order

International Standard Serial Number (ISSN)

1539-6746

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 International Press of Boston, Inc., All rights reserved.

Publication Date

01 Aug 2019

Link to Full Text

Share

 
COinS