A robust low-Mach solver for phase-changing flows

We extended a previously developed VoF-based numerical method for phase-changing flows (Scapin N. et al., J. Comput. Physics, 2020) to solve the governing equations in the limit of zero Mach number. Compared to the fully compressible formulation, the proposed methodology has three distinct advantages. First, it is able to relax the assumption of constant thermophysical properties while effectively filtering the acoustic effects and the associated stringent numerical time-step restrictions. Next, the hydrodynamic pressure is still governed by an elliptic equation for which FFT-based solvers can be employed. Finally, the divergence constrain of the velocity field can be imposed up to machine precision provided that the thermodynamic pressure and the thermophysical properties are updated consistently. The algorithm is implemented on top of a second order accurate two-fluid Navier-Stokes solver coupled with an algebraic volume of fluid method (MTHINC), and extended with the corresponding transport equations for the vaporized liquid mass and thermal energy. Finally, the robustness of the method for more demanding simulations is assessed in two configurations: evaporating droplets in homogeneous turbulent flows and evaporating two-layer Rayleigh-Bernard turbulence.