A Numerical Method for Two-Phase Flow Based on a Phase-Field Model

For interface-tracking simulation of incompressible two-phase fluids with high density ratios, a new numerical method was proposed by combining Navier-Stokes equations with a phase-field model based on a van der Waals-Cahn-Hilliard free-energy theory. The method was applied to several benchmark problems. Major findings are as follows: (1) The volume flux derived from a local chemical potential gradient in the Cahn-Hilliard equation leads to accurate volume conservation, autonomic reconstruction of gas-liquid interface, and reduction of numerical diffusion and oscillation. (2) The proposed method gave good predictions of pressure increase inside a bubble caused by the surface tension force. (3) A single liquid drop falling in stagnant gas and merging into a stagnant liquid film was successfully simulated.