A hierarchy of hyperbolic models linking Boltzmann to Navier Stokes equations for polyatomic gases

The paper describes and extends to polyatomic gases a general strategy for building a hierarchy of numerical models relating the Boltzmann and the Navier-Stokes equations. It is based on two recent mathematically consistent ansatz, namely gaussian BGK collision models and Levermore's moment expansions, and preserves entropy, hyperbolicity, and relaxation constants. We can then adapt the general adaptive algorithm previously developed for coupling Navier-Stokes equations to local kinetic models. In this process, the Navier-Stokes equations are obtained by a Hilbert asymptotic expansion of the moment's equations, which gives them a kinetic interpretation in terms of a positive distribution function associated to the fifteen moments used in Levermore's expansion.