Highly efficient and unconditionally energy stable semi-discrete time-marching numerical scheme for the two-phase incompressible flow phase-field system with variable-density and viscosity (Q2106847)

The authors consider the numerical approximation of the variable-density/viscosity CH-NS (Cahn-Hilliard-Navier-Stokes model) of an incompressible binary fluid flow system. One of the main facts to deal with is the approximation of the nonlinear coupling terms contained in the model. A novel fully-decoupled numerical scheme is developed which can achieve unconditional energy stability while explicitly discretizing nonlinear coupling items. The scheme is semi-discrete time-marching and it needs to solve a series of completely independent linear elliptic equations at each time step, in which the Cahn-Hilliard equation and the pressure Poisson equation are the constant coefficient. Some numerical tests are presented to show the effeciency of the proposed scheme.