We present a new numerical formulation governing the physics of a plasma near strong shock waves in gases at hypersonic speeds. A plasma is composed of multiple species in thermo-chemical nonequlibrium, thus making high-fidelity numerical modeling challenging. In order to reduce the size and complexity of the problem, a number of simulation approaches take advantage of simplifications concerning the flow properties of the various species. The plasma is also often assumed to be charge neutral in

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... order to bypass the requirement of the solution of Maxwell's equations. In this work, we drop these simplifications and solve the full Navier-Stokes equations for each species in the plasma including the physics of thermo-chemical nonequilibrium, along with Maxwell's equations to account for electrodynamic e↵ects. The full set of equations has been programmed in the "Stanford University Unstructured" (SU 2 ) open source suite of tools, and two di↵erent test cases have been simulated and compared with published data. In the first case, the unsteady dynamics of plasma formation near a normal shock wave at Mach 15 are modeled and compared with previous work. In the second case, heat transfer to a three dimensional body from a stream of plasma at Mach 4.6 is simulated and compared with experimental data. The two test cases show an excellent match with published data. In addition to this validation / verification study, this paper also presents the formulation and numerical implementation of our model for the equations governing high-temperature plasmas.