Numerical Approximations for the Hydrodynamics Coupled Binary Surfactant Phase Field Model: Second-Order, Linear, Unconditionally Energy Stable Schemes
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.
C. Xu et al., "Numerical Approximations for the Hydrodynamics Coupled Binary Surfactant Phase Field Model: Second-Order, Linear, Unconditionally Energy Stable Schemes," Communications in Mathematical Sciences, vol. 17, no. 3, pp. 835-858, International Press of Boston, Inc., Aug 2019.
The definitive version is available at https://doi.org/10.4310/CMS.2019.v17.n3.a10
Mathematics and Statistics
Keywords and Phrases
Cahn-Hilliard; Energy stability; fluid-surfactant; Navier-Stokes; Phase-field; Second order
International Standard Serial Number (ISSN)
Article - Journal
© 2019 International Press of Boston, Inc., All rights reserved.
01 Aug 2019