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


Gorban, Alexander N. and Karlin, Iliya V. (2005) Invariance correction to Grad's equations: where to go beyond approximations? Continuum Mechanics and Thermodynamics, 17, (4), pp. 311-335. (doi:10.1007/s00161-005-0202-z).

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Description/Abstract

We review some recent developments of Grad's approach to solving the Boltzmann equation and creating a reduced description. The method of the 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 of the method of the 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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1007/s00161-005-0202-z
ISSNs: 0935-1175 (print)
Keywords: Boltzmann equation, invariant manifolds, kinetic models, Lattice Boltzmann method, microflow
Subjects:
ePrint ID: 49235
Date :
Date Event
30 August 2003Submitted
December 2005Published
Date Deposited: 25 Oct 2007
Last Modified: 16 Apr 2017 18:18
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/49235

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