A kinetic description of anisotropic fluids with multivalued internal energy

This work is concerned with some extensions of the classical compressible Euler model of fluid dynamics in which the fluid internal energy is a measure-valued quantity. A first extension was derived from the hydrodynamic limit of a kinetic model involving a specific class of collision operators typical from quasi-linear plasma theory (see Eur. J. Mech. B Fluids 20 (2001) 303–327, and Contin. Mech. Thermodyn. 10 (1998) 153–178). In these papers the collision operator simply describes the isotropization of the kinetic distribution function about some averaging velocity. In the present work we introduce a new extension of such models in which the relaxed distribution is anisotropic. Similarly to (Eur. J. Mech. B Fluids 20 (2001) 303– 327) and (Contin. Mech. Thermodyn. 10 (1998) 153–178) this model is derived from a kinetic equation with a collision operator that relaxes to anisotropic equilibria. We then investigate diffusive corrections of this fluid-dynamical model using Chapman– Enskog techniques and show how the anisotropic character affects the expression of the viscosity and of the heat flux.  2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.