An all-Mach, low-dissipation strategy for simulating multiphase flows

Abstract Liquid-gas flows that involve compressibility effects occur in many engineering contexts, and high-fidelity simulations can unlock further insights and developments. Introducing several numerical innovations, this work details a collocated, volume-of-fluid, finite volume flow solver that is robust, conservative, and capable of simulating flows with shocks, liquid-gas interfaces, and turbulence. A novel hybrid advection scheme provides stability while minimizing dissipation. An unsplit semi-Lagrangian method provides the robustness and precision to handle discontinuities in the flow, and a centered scheme eliminates numerical kinetic energy dissipation elsewhere, allowing accurate simulation of turbulence. A pressure projection scheme makes multiphase compressible simulations much less costly, and formulating this projection as incremental reduces numerical dissipation further. Local relaxation to mechanical equilibrium is used to properly solve for the pressure and energy fields in multiphase contexts. Within this framework, a consistent methodology for implementing multiphase pressure projection is derived, including surface tension. The complete algorithm is validated with benchmark tests in one, two, and three dimensions that evaluate the accuracy and stability of the approach in predicting compressible effects, turbulent dissipation, interface dynamics, and more through comparisons with theory, experiments, and reference simulations. Finally, the utility of the numerical approach is demonstrated by simulating an atomizing liquid jet in a Mach 2 crossflow.