A second-order time stepping scheme is developed for the binary
fluid-surfactant phase field model coupled with hydrodynamics by using
the scalar auxiliary variable approach and pressure correction method.
The free energy contains a double-well potential, a nonlinear coupling
entropy and a Flory-Huggins potential. By introducing one scalar
auxiliary variable, the system is transformed into an equivalent form so
that the nonlinear terms can be treated semi-explicitly. The scheme is
linear and decoupled; thus, they can be solved eciently. We further
prove that the semidiscretized scheme in time is unconditionally energy
stable. Numerical experiments are performed to validate the accuracy and
energy stability of the proposed scheme.