Fully decoupled pressure projection scheme for the numerical solution of diffuse interface model of two-phase flow

We describe a fully decoupled finite difference approach for solving the Cahn–Hilliard Navier–Stokes (CHNS) model of two-phase flow. The governing equations consist of the incompressible Navier–Stokes equations coupled with the nonlinear Cahn–Hilliard equation through surface tension. The coupled system of equations is decoupled with the help of an intermediate velocity-field. The spatial discretization is carried out by finite differences while the explicit Euler's method is used for the temporal part. The decoupling feature of the method makes the numerical implementation easy. Several two-phase flow problems have been numerically simulated in order to test the method's efficacy.