Physically consistent formulations of split convective terms for turbulent compressible multi-component flows

Abstract

We analyse the properties and characteristics of kinetic-energy-preserving, entropy-preserving, and pressure-equilibrium-preserving split convective forms for compressible multi-component flows. The results show that such schemes offer improved pressure-equilibrium-preserving properties and numerical stability compared to most other existing schemes, but also that the preservation of pressure equilibrium is not guaranteed for flows with varying specific heats. Furthermore, for the convective terms in species mass fraction transport equations, some split forms may fail to preserve key physical properties discretely. We construct a formulation for the species convective terms that consistently maintains these key physical properties, including species mass conservation, uniform mass fraction preservation, and temperature-equilibrium preservation. The capability of the proposed scheme in maintaining these properties is demonstrated analytically and tested in one-dimensional advection problems. Last, the proposed scheme is compared with schemes that do not satisfy these properties in under-resolved simulations of a modified inviscid Taylor–Green vortex flow. The results show improved performance of the proposed scheme and highlight the importance of a convective scheme for the species mass fractions to be able to consistently preserve these physical properties in a discrete sense.