A multi-temperature TVD algorithm for relaxing hypersonic flows

In this paper, the extension of a multispecies TVD algorithm, second-order accurate for real-gas flows to a multitemperature formulation is described. The convection algorithm is coupled to internal relaxation processes, and the features of the coupling are examined. The first version consists of a three-temperature model, where translational-rotational, vibrational, and electronic energy modes are separately convected. Although several species are present, there is only one vibrational temperature in this model. The second version generalizes to a vibrational temperature for each molecular specie, with additional couplings between species. The algorithms are applied to a generic two-dimensional flow field, and results are compared with experimental observations.