A weakly compressible scheme with a diffuse-interface method for low Mach number two-phase flows

A weakly compressible scheme for gas–liquid two-phase flows with low Mach number is proposed for a fully-explicit time integration. The scheme is based on the fractional-step method with the Euler equation solver and time integration for viscous, surface tension and gravity terms. For the efficient solution of the Euler equation, we introduce the directional-splitting method and the method of characteristics which is applicable to semi-Lagrangian methods. A reduction of the speed of sound is also taken into consideration to enlarge the time step intervals. The primitive flow variables are time-integrated on the node-center configuration. To capture the gas–liquid interface, the conservative phase-field equation is solved by using the multi-moment method. It is computed as a conservative form for the volume-averaged value defined at the cell center, in which the flow velocities are given on the node. We discard the exact momentum conservation, however the total mass of gas and liquid is conserved by introducing a phase-field variable. Several benchmark problems are examined and the results of the explicit scheme are in good agreement with the experimental and computational references.