Abstract
We develop a two-phase flow model for solving the nonlinear level set (LS) equation and Navier-Stokes equations in two dimension. In the proposed one-step LS method, the sharp interface is captured by implicitly representing the zero LS contour. The nonlinear LS equation is solved by upwinding Combined Compact Difference (CCD) scheme for the convection terms and center difference scheme for the other terms in space for predicting propagation of interface. Within the framework of Navier-Stokes solver, the semi-implicit Gear algorithm on a semi-staggered fixed grid is used for velocity-pressure coupling. The interface normal and curvature are calculated in terms of a hyperbolic tangent profile across the interface. To verify the proposed LS method, we consider reversed single vortex and Zalesak’s cases which are amenable to exact solutions. The proposed two-phase model is also investigated by solving the dam-break, Rayleigh-Taylor instability and bubble rising problems.
Disclosure statement
We declare no conflicts of interest to this work.