Computation of hypersonic shock waves in diatomic gases using the generalized Boltzmann Equation

The paper describes the methodology for computing hypersonic non-equilibrium shock wave flows of diatomic gases using the Generalized Boltzmann Equation (GBE) including both the vibrational - translational (VT) and rotational - translational (RT) relaxations. For the VT relaxation, GBE is always solved. For the RT relaxation, two approaches are employed. In the first approach, for the RT relaxation GBE is solved. This approach is computationally very intensive since it requires solving the complete GBE for both vibrational and rotational degrees of freedom. In the second approach, a two-level BGK type model of RT relaxation is employed. The second approach is much more efficient than the first (about 20 times faster). The paper describes the twolevel RT relaxation model. The model is validated by computing the shock structure at high Mach numbers by comparing the results with the complete GBE solution. Computations are then performed for the shock structure accounting for both the vibrational and rotational excitations, using the second approach for the RT relaxations.