Weakly compressible Navier-Stokes solver based on evolving pressure projection method for two-phase flow simulations

Abstract

An evolving pressure projection method for numerical computations of the weakly compressible Navier-Stokes equations is proposed. Fully explicit time integration is achieved using an independent pressure evolution equation. To damp the acoustic wave in a weakly compressible fluid flow, we iteratively compute the pressure evolution equation coupled with a projection step. Due to the simplicity and locality of this iteration procedure, it does not increase the computational amount too much. The computation is performed on a staggered Cartesian grid. By introducing the phase field model for interface capturing, this solver can be directly applied to two-phase flow simulations using a one-fluid model. Exact mass conservation is ensured by a finite-volume formulation of the conservative phase field equation. Various benchmarking problems are simulated to validate accuracy. The stability of a violent two-phase flow with large density and viscosity ratio is demonstrated in a three-dimensional dam break simulation. Numerical results show that the proposed method for weakly compressible Navier-Stokes equations can prevent oscillations of pressure and velocity.