Approximately pressure-equilibrium-preserving scheme for fully conservative simulations of compressible multi-species and real-fluid interfacial flows

This study proposes a numerical method for fluid interfaces in compressible multi-species and real-fluid flow simulations. The proposed method preserves the full conservation (species-mass, momentum, and energy) property of compressible flow equations while approximately maintaining the pressure equilibrium condition at fluid interfaces. The numerical fluxes of internal energy and species-mass are newly constructed to satisfy the pressure equilibrium condition approximately. The modified equation for the pressure equilibrium condition shows that the proposed numerical fluxes introduce different coefficients in the second-order error term, compared to standard numerical fluxes, thereby reducing the pressure equilibrium error. The conservation and pressure equilibrium properties of the proposed method are validated through one-dimensional and two-dimensional smooth interface advection problems using the compressible multi-species Euler equations with the Soave-Redlich-Kwong equation of state.