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A computationally accurate and efficient numerical method under a unifiedframework is crucial to various multi-scale scientific and engineeringproblems. So far, many numerical methods have encountered various challenges inefficiently solving multi-scale non-equilibrium flows that cover a wide rangeof Knudsen numbers, especially the three-dimensional hypersonic flows. In thisstudy, a conservative implicit scheme is further presented forthree-dimensional steady flows of diatomic gases in all flow regimes, whereboth the implicit microscopic kinetic equations based on Rykov model and thecorresponding implicit macroscopic governing equations are solvedsynchronously. Furthermore, a simplified multi-scale numerical flux inspired bythe strategy of discrete unified gas kinetic scheme (DUGKS) is proposed torelieve the limitation of grid size and time step in all flow regimes. The fluxis constructed through a backward Euler difference scheme with theconsideration of collision effect in the physical reconstruction of the gasdistribution function on the cell interface. Meanwhile, its asymptoticpreserving property in the continuum limit is analyzed. In order to pursue highcomputational efficiency in three-dimensional flow simulations, theunstructured discrete velocity space (DVS) and MPI parallel in DVS are adoptedto further speed up the calculation. Additionally, based on numericalexperiments of Apollo 6 command module, an empirical generation criterion forthree-dimensional unstructured DVS is proposed. Numerical results indicatethat, the present method is about one to two orders of magnitude faster thanthe explicit conserved DUGKS method. The present method is proved to accuratelyand efficiently predict aerothermodynamic properties of hypersonic rarefied gasflows.

A conservative implicit scheme for three-dimensional steady flows of  diatomic gases in all flow regimes using unstructured meshes in the physical  and velocity spaces