From hyperbolic regularization to exact hydrodynamics for linear Grad System
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
The derivation of hydrodynamics from a microscopic description is the classical problem of physical kinetics. The Chapman-Enskog method derives the solution from the Boltzmann equation in the form of a series in powers of Knudsen number, where is the ratio between the particle mean free path and the length scale of variations of hydrodynamic fields. However, as first demonstrated by Bobylev for Maxwells molecules, even in the simplest case (one-dimensional linear deviation from global equilibrium), the Burnett and the super-Burnett hydrodynamics violate the basic physics behind the Boltzmann equation. Namely, the acoustic contributions at sufficiently short wave-lengths increase with time instead of decaying. Inspired by a recent hyperbolic regularization of Burnetts hydrodynamic equations, we introduce a method to derive stable equations of linear hydrodynamics to any desired accuracy in Knudsen number, starting from a simple kinetic model a thirteen Moments Grad System. We show that stability arises as interplay between two basic features of the resulting hydrodynamic equations, i.e. hyperbolicity and dissipativity.