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), 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)
Related URLs:
Keywords: Boltzmann equation, invariant manifolds, kinetic models, Lattice Boltzmann method, microflow
Subjects: T Technology > TJ Mechanical engineering and machinery
T Technology > TA Engineering (General). Civil engineering (General)
Divisions : University Structure - Pre August 2011 > School of Engineering Sciences > Thermofluids and Superconductivity
ePrint ID: 49235
Accepted Date and Publication Date:
Status
December 2005Published
30 August 2003Submitted
Date Deposited: 25 Oct 2007
Last Modified: 31 Mar 2016 12:26
URI: http://eprints.soton.ac.uk/id/eprint/49235

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