Computation of hypersonic shock waves in inert gas mixtures using the generalized Boltzmann equation

For numerical solution of the Generalized Boltzmann Equation (GBE) when simulating rarefied hypersonic flows in a gas mixture of multiple species, the GBE is formulated in the impulse space. The gas mixtures may consist of both monatomic gases and diatomic gases with arbitrary constituents, concentrations, and mass ratios. The conservative discrete ordinates method of Tcheremissine is applied to validate the solutions against the existing simulations for shock waves in an inert binary mixture of monoatomic gases. The method is then exercised for various concentration ratios, mass ratios, and density ratios to evaluate its ability to simulate a wide range of binary gas mixtures. The method is then applied to simulate two of the three primary constituents of air (N₂, O₂, Ar) in a binary mixture at 1:1 concentrations and at the relative concentrations found in air. These solutions can serve as validation test cases for other methods as well as an important building block in developing complex 3D simulations for shock waves in a mixture of multiple gases.