Unified gas-kinetic scheme for diatomic molecular simulations in all flow regimes

A unified gas-kinetic scheme (UGKS) is constructed for both continuum and rarefied flow computations. The underlying principle for the development of UGKS is the direct modeling for the gas evolution process from the kinetic to the hydrodynamic scale, which is used in the flux construction across a cell interface. More specifically, the physical process from the kinetic particle free transport to the hydrodynamic pressure wave propagation is recovered in the flux function. In the previous study, the UGKS has been developed mainly for monatomic gas with particle translational motion only. The construction of time evolution solution is based on the BGK, Shakhov, and ES-BGK models. The UGKS has been validated through extensive numerical tests. In this paper, a UGKS for diatomic gas will be constructed, where the gas-kinetic Rykov model with a Landau-Teller-Jeans-type rotational energy relaxation is used in the numerical scheme. The new scheme will be tested in many cases, such as homogeneous flow relaxation, shock structure calculations, hypersonic flow passing a flat plate, and the flow around a blunt circular cylinder. The analytic, DSMC, and experimental measurements will be used for validating the solutions of UGKS.