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An implicit scheme for steady state solutions of diatomic gas flow ispresented. The method solves the Rykov model equation in the finite volumediscrete velocity method (DVM) framework, in which the translational androtational degrees of freedom are taken into account. At the cell interface, adifference scheme of the model equation is used to construct a multiscale flux(similar to discrete unified gas-kinetic scheme (DUGKS)), so that the cell sizeis not constrained by the cell Knudsen (Kn) number. The physical local timestep is implemented to preserve the multiscale property in the nonuniform-meshcase. The implicit macroscopic prediction technique is adopted to find apredicted equilibrium state at each time level and the implicit macroscopicgoverning 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 forparticle velocity space. In the test cases, the unstructured velocity-spacemesh is used, the present method is proved to be efficient and accurate.

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