Fully conservative and pressure-equilibrium preserving scheme for compressible multi-component flows

Abstract

In compressible flows with a variable ratio of specific heats, such as multi-component flows, the conventional conservative schemes generate spurious pressure oscillations at multi-component interfaces even when the interfaces are smooth. In this study, we propose a novel spatial discretization scheme that maintains both the primary conservation and pressure equilibrium in discontinuity-free compressible multi-component flows. The key to this study is the compatibility condition, which is the discrete condition for implicitly satisfying the pressure equilibrium at the discrete level. The compatibility condition is derived based on the analytical relation between the mass of species and the ratio of specific heats in the governing equations. The proposed scheme is constructed by the spatial discretization that satisfies the compatibility condition and can be applied to the arbitrary number of species components. The inviscid smooth interfaces advection problems verify that the proposed scheme satisfies both the pressure equilibrium and primary conservation only by solving the conservation equations, unlike the existing schemes that solve non-conservative or overspecified equations.