Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model (Communications in Computational Physics, 2020)
Here, we develop a first and a second order time stepping schemes for a binary fluid-surfactant phase field model by using the scalar auxiliary variable approach.The free energy contains a double-well potential, a nonlinear coupling entropy and aFlory-Huggins potential. The resulting coupled system consists of a Cahn-Hilliardtype equation and a Wasserstein type equation which leads to a degenerate problem.By introducing only one scalar auxiliary variable, the system is transformed into anequivalent form so that the nonlinear terms can be treated semi-explicitly. Both theschemes are linear and decoupled, thus they can be solved efficiently. We further provethat these semi-discretized schemes in time are unconditionally energy stable. Somenumerical experiments are performed to validate the accuracy and energy stability ofthe proposed schemes.
Keywords: Binary fluid-surfactant; scalar auxiliary variable approach; unconditional energy stability; linear scheme; decoupled.