A conservative implicit scheme for steady state solutions of diatomic gas flow in all flow regimes

Abstract

An implicit scheme for steady state solutions of diatomic gas flow is presented. The method solves the Rykov model equation in the finite volume discrete velocity method (DVM) framework, in which the translational and rotational degrees of freedom are taken into account. At the cell interface, a difference scheme of the model equation is used to construct a multiscale flux (similar to discrete unified gas-kinetic scheme (DUGKS)), so that the cell size is not constrained by the cell Knudsen (Kn) number. The physical local time step is implemented to preserve the multiscale property in the nonuniform-mesh case. The implicit macroscopic prediction technique is adopted to find a predicted equilibrium state at each time level and the implicit macroscopic governing equation is solved along with the implicit microscopic system. Furthermore, an efficient integral error compensation technique is applied, which makes the scheme conservative and allows more flexible discretization for particle velocity space. In the test cases, the unstructured velocity-space mesh is used, the present method is proved to be efficient and accurate.