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A two kinetic temperature displaced Maxwellian is used as the weight function for a Hermite expansion of the distribution function. The expansion is cut up to fourteen moments following Grad's theory. The moment equations are used to derive under a Knudsen type expansion what one may call two-temperature Navier-Stokes equations (2T-NS). The 2T-NS equations are then solved numerically, for a plane shock wave, and a comparison between Navier-Stokes, Holian theory, and results from molecular dynamics and Monte Carlo is performed.
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Uribe et al. (1998) studied this question.
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