The unique physics associated with flying at hypersonic speeds create a challenging operational environment for any prospective vehicle design.  From an aerodynamics standpoint, the incredibly high temperatures encountered in this environment pose a significant thermal loading on the vehicle and excite internal vibrational energy modes within the gas molecules themselves that can lead to dissociation and other chemical reactions in the air and on the vehicle surface.  From a propulsion standpoint, the most efficient means of generating thrust is using an air-breathing engine, which requires stabilizing a flame under highly adverse supersonic (or high-subsonic) flow speeds within the combustor. This opportunity is focused on elucidating the basic physics underpinning hypersonic vehicle aerodynamics and propulsion technologies by developing numerical methods capable of simulating the complex, non-equilibrium, and chemically-reacting flows that drive these systems.  Potential topics include transition to turbulence in hypersonic boundary layers, high-temperature air chemical kinetics, non-equilibrium and rarefied gas flows, surface ablation, shock-turbulence interaction, hypervelocity impact of water and ice particulates, droplet and crystal breakup in high-shear flows, fluid-structure interactions, pyrolysis of heterogeneous solid fuels, particulate and droplet combustion, flame holding within a scramjet, gas-phase radiation transport, and magnetohydrodynamics of wake turbulence.