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Hydrodynamics from Grad's equations: What can we learn from exact solutions?
Author(s) -
Karlin I.V.,
Gorban A.N.
Publication year - 2002
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/1521-3889(200211)11:10/11<783::aid-andp783>3.0.co;2-v
Subject(s) - nonlinear system , moment (physics) , mathematics , basis (linear algebra) , classical mechanics , physics , mathematical analysis , statistical physics , geometry , quantum mechanics
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, Padé approximants, and invariance principle are compared both in linear and nonlinear situations.