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

A conservative implicit scheme in the finite volume discrete velocity method framework is proposed for solving the three-dimensional steady flows of molecular gases in all flow regimes from continuum one to free-molecular one. This work is based on the Boltzmann-Rykov model equation, which is a nonlinear relaxation model and can describe the thermodynamic non-equilibrium of diatomic gas flows. The macroscopic equations are solved implicitly together with the Rykov model equation to find a predicted equilibrium distribution first at each iteration step. As a result, the collision term of the Rykov model equation can be discretized in a fully implicit way for fast convergence in all flow regimes. At the cell interface, an asymptotic preserving simplified multi-scale numerical flux is developed to relieve the limitation of grid size and time step in all flow regimes, which can keep the multi-scale property and achieve high computational efficiency. The integral error compensation technique is used to keep the scheme conservative and greatly reduce the number of unstructured discrete velocity space (DVS) meshes. Furthermore, an empirical criterion based on the numerical experiments of the Apollo 6 command module is suggested to guide the generation of three-dimensional unstructured DVS. The accuracy and efficiency of the present method are demonstrated by a number of three-dimensional classic cases, covering different flow regimes.