Strictly Entropy-Conserving Seven-Equation Based Keep Scheme Coupled With Phase-Field Method for Compressible Two-Phase Flows

The numerical simulations of compressible two-phase flows are prone to numerical insta- bilities due to the presence of large density ratios and sharp gradients at the interface. While these instabilities have been alleviated by introducing significant numerical viscosity in the past, such numerical dissipation smears out small-scale vortex structures, degrading the quality of high-fidelity two-phase turbulent flow simulations. To overcome this fundamental and critical drawback, this study proposes Kinetic Energy and Entropy Preserving (KEEP) scheme for compressible two-phase flows, which achieves both robust and non-dissipative properties by satisfying the conservation of kinetic energy and entropy at the discrete level. We employ the seven-equation model by Baer & Nunziato [1] as the governing equations and analyze the en- tropy conservation error to derive the strictly entropy-conserving numerical fluxes. To this end, we tested the proposed scheme through numerical experiments, including one-dimensional (1D) interface and density advection and three-dimensional (3D) two-phase Taylor-Green vortex. In particular, the 3D two-phase Taylor-Green vortex case is, to the best of our knowledge, the first to solve inviscid compressible two-phase turbulence without numerical dissipation, even when using high density ratios and realistic stiffened-gas Equation of State (EOS) parameters.