A kinetic energy–and entropy-preserving scheme for compressible two-phase flows

Accurate numerical modeling of compressible flows, particularly in the turbulent regime, requires a method that is non-dissipative and stable at high Reynolds (Re) numbers. For flow, it known discrete conservation kinetic energy not sufficient condition for stability, unlike incompressible flows. In this study, we adopt recently developed conservative diffuse-interface (Jain et al., 2020 [30]) simulation two-phase This discretely conserves mass each phase, momentum, total system consistently reduces to single-phase Navier-Stokes when properties two phases are identical. We here propose consistency conditions between fluxes, such any set fluxes satisfy these would spuriously contribute entropy system. also present fluxes—which satisfies conditions—that results an exact approximate absence pressure work, viscosity, thermal diffusion effects, time-discretization errors. Since model identical, proposed applicable broader class To end, coarse-grid simulations flows infinite Re, illustrate stability canonical test cases, as isotropic turbulence Taylor-Green vortex A higher-resolution droplet-laden decaying presented, effect presence droplets on flow analyzed.