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

An implicit scheme for steady state solutions of diatomic gas flow is presented. The Rykov model equation is solved in the finite volume discrete velocity method 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), so that the cell size is not constrained by the cell Knudsen 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 step, making the scheme highly efficient in all flow regimes. Furthermore, an integral error compensation technique with negligible computational cost is proposed, which makes the scheme conservative and allows more flexible discretization for particle velocity space. With the compensation technique, the unstructured velocity-space mesh is used in the test cases, which reduces the velocity mesh number significantly. The present method is proved to be efficient and accurate.