Fully conservative scheme for multi-component flows satisfying pressure equilibrium

In compressible flows with a non-constant ratio of specific heats (i.e., multi-component or supercritical flows), it is well-known that numerical simulation with general conservative equations generates spurious pressure oscillations. This study proposes a fully conservative scheme that satisfies the pressure equilibrium for compressible multi-component flows. The idea is the spatial discretization describes the transport of the specific heats with only the conservative governing equations and without additional equations. In contrast to the previous studies that solve non-conservative or overspecified equations, the proposed scheme preserves pressure equilibrium by solving only conservation equations for mass, momentum, total energy, and mass of species.