We present a BGK-type collision model which approximates, by a Chapman-Enskog expansion, the compressible Navier-Stokes equations with a Prandtl number that can be chosen arbitrarily between 0 and 1. This model has the basic properties of the Boltzmann equation, including the H-theorem, but contains an extra parameter in comparison with the standard BGK model. This parameter is introduced multiplying the collision operator by a nonlinear functional of the distribution function. It is adjusted to the Prandtl number.

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