BGK-Based Scheme for Multicomponent Flow Calculations

Abstract

This paper concerns the extension of the gas-kinetic BGK-type scheme to multicomponent flow calculations. In this new scheme, each component satisfies its individual gas-kinetic BGK equation and the equilibrium states for each component are coupled in space and time to have common temperature and velocity. The particle diffusion in gas mixtures is included naturally in the gas-kinetic model. The current scheme can handle strong shocks and be oscillation-free through the material interface. The scheme guarantees the exact mass conservation for each component and the exact conservation of total momentum and energy in the whole particle system. As a special application, the current scheme is applied to gas vacuum interaction case, where the mass densities for other components are set to zero in the whole domain. The extension of the current approach to three dimensions is straightforward. With the definition of ϕ = ρ(1)− ρ(2)in the two-component gas flow, similar to the level set method we can follow explicitly the time evolution of the material interface (ϕ = 0). The numerical results confirm the accuracy and robustness of the BGK-type scheme.