Hydrodynamics from Grad's equations: What can we learn from exact solutions?
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.
Keywords
Cite
@article{arxiv.cond-mat/0209560,
title = {Hydrodynamics from Grad's equations: What can we learn from exact solutions?},
author = {Iliya V. Karlin and Alexander N. Gorban},
journal= {arXiv preprint arXiv:cond-mat/0209560},
year = {2012}
}
Comments
61 pages. Slightly edited and corrected version. It follows mostly Chapter 8 of the book: Gorban, A.N. and Karlin, I.V., Invariant Manifolds for Physical and Chemical Kinetics, Lect. Notes Phys. 660, Springer, Berlin, Heidelberg, 2005