Linear and Unconditionally Energy Stable Schemes for the binary Fluid-Surfactant Phase Field Model
This work provides efficient numerical methods for simulating binary fluid-surfactant systems, which are important in materials science and fluid dynamics, but the contribution is incremental as it applies existing IEQ methodology to a specific model.
The authors developed linear, unconditionally energy stable first- and second-order time marching schemes for a binary fluid-surfactant phase field model using the Invariant Energy Quadratization approach. Numerical experiments in 2D and 3D validated the accuracy and energy stability of the schemes.
In this paper, we consider the numerical solution of a binary fluid-surfactant phase field model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg-Landau double well potential, and a logarithmic Flory-Huggins potential. The resulting system consists of two coupled, nonlinear Cahn-Hilliard type equations. We develop a set of first and second order time marching schemes for this system using the "Invariant Energy Quadratization" approach, in particular, the system is transformed into an equivalent one by introducing appropriate auxiliary variables and all nonlinear terms are then treated semi-explicitly. Both schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable in the discrete sense. Various 2D and 3D numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.