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Hydrodynamics from Grad's equations: What can we learn from exact solutions?

Gorban A. N., Karlin I. V.
arXiv:cond-mat/0209560 v1 24 Sep 2002

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Full text of the article [pdf, 418 Kb, in english]

Abstract

A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad's moment equations. Grad's systems are considered as the minimal kinetic models where the Chapman-Enskog method can be studied exactly, thereby providing the basis to compare various approximations in extending the hydrodynamic description beyond the Navier-Stokes approximation. Various techniques, such as the method of partial summation, Pad_e approximants, and invariance principle are compared both in linear and nonlinear situations.