Invariance correction to Grad's equations: Where to go beyond approximations?

Details Invariance correction to Grad's equations: Where to go beyond approximations? Invariance correction to Grad's equations: Where to go beyond approximations?

2005-04-09

arxiv.org/abs/cond-mat/0504221v1

Continuum Mech. Thermodyn. (2005) 17(4): 311--335.

Physics

Condensed Matter

Statistical Mechanics

35 pages, a review paper, Continuum Mechanics and Thermodynamics, in press

Scientific paper

10.1007/s00161-005-0202-z

We review some recent developments of Grad's approach to solving the Boltzmann equation and creating reduced description. The method of invariant manifold is put forward as a unified principle to establish corrections to Grad's equations. A consistent derivation of regularized Grad's equations in the framework the method of invariant manifold is given. A new class of kinetic models to lift the finite-moment description to a kinetic theory in the whole space is established. Relations of Grad's approach to modern mesoscopic integrators such as the entropic lattice Boltzmann method are also discussed.

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