Kinetic energy and entropy preserving (KEEP) scheme for compressible multi-component flows

Flows of multiple species with different properties are important physical phenomena in many engineering applications. Simulations of multi-component flows often lead to numerical instability around the interface due to the steep variations in the flow properties. While this instability can be mitigated by introducing numerical dissipation, it is crucial to minimize (ideally zero) the numerical dissipation in high-fidelity turbulent flow simulations, highlighting the need for non-dissipative and robust numerical methods. This study proposes non-dissipative and robust spatial discretization schemes for discontinuity-free compressible multi-component flows. In addition to the primary conservation for the mass of each species, momentum, and total energy, the secondary preservation of the kinetic energy and entropy is considered, and the kinetic energy and entropy preserving (KEEP) scheme, originally developed for single component flows, is extended to multi-component flows. Based on the entropy conservation error analysis, the entropy conservative numerical fluxes are derived, and their pressure-equilibrium-preservation property is discussed.