Satisfying conservation and pressure equilibrium in compressible multi-component flow simulation: a novel discretely compatible scheme

The mixing of fluid components is a crucial physical phenomenon in engineering applications. While the pressure equilibrium at the fluid interface is the physics of inviscid flows without surface tension, the conventional conservative schemes generate spurious pressure oscillations at the interface, thus violating the physics of pressure equilibrium. In this study, we propose a fully conservative and pressure-equilibrium preserving scheme for compressible multi-component flows. We first derive the compatibility condition that describes a condition for implicitly satisfying the pressure equilibrium at the discrete level. Then, we propose a novel scheme that satisfies the compatibility condition. Unlike conventional non-conservative or over-specifying equilibrium preserving schemes, the proposed scheme satisfies both the primary conservation (i.e., the conservation of mass of each species, momentum, and total energy) and pressure-equilibrium preservation. To the authors' knowledge, there is no scheme proposed that maintains the pressure equilibrium by solving only the conservative equations without an additional overspecified equation.