Karlin, I.V. and Gorban, A.N. (2002) Hydrodynamics from Grad's equations: What can we learn from exact solutions? Annalen der Physik, 11 (10-11), 783-833. (doi:10.1002/1521-3889(200211)11:10/11<783::AID-ANDP783>3.0.CO;2-V).
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, Pade approximants, and invariance principle are compared both in linear and nonlinear situations.
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