Numerical approximations for the binary Fluid-Surfactant Phase Field Model with fluid flow: Second-order, Linear, Energy stable schemes
For researchers simulating complex fluid-surfactant systems, this provides efficient and stable numerical methods, though incremental as it extends existing IEQ and projection techniques to a coupled model.
The paper develops two linear, second-order, unconditionally energy stable numerical schemes for a binary fluid-surfactant phase-field model coupled with fluid flow, combining IEQ, projection method, and IMEX treatment. Numerical experiments in 2D and 3D validate accuracy and energy stability.
In this paper, we consider numerical approximations of a binary fluid-surfactant phase-field model coupled with the fluid flow, in which the system is highly nonlinear that couples 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.