Invariance correction to Grad's equations: where to go beyond approximations?
Invariance correction to Grad's equations: where to go beyond approximations?
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.
Boltzmann equation, invariant manifolds, kinetic models, Lattice Boltzmann method, microflow
311-335
Gorban, Alexander N.
31914661-757a-4b6b-a953-109ac7499746
Karlin, Iliya V.
3331716f-692a-4b81-87a4-9aad489d025d
December 2005
Gorban, Alexander N.
31914661-757a-4b6b-a953-109ac7499746
Karlin, Iliya V.
3331716f-692a-4b81-87a4-9aad489d025d
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), .
(doi:10.1007/s00161-005-0202-z).
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.
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Submitted date: 30 August 2003
Published date: December 2005
Keywords:
Boltzmann equation, invariant manifolds, kinetic models, Lattice Boltzmann method, microflow
Identifiers
Local EPrints ID: 49235
URI: http://eprints.soton.ac.uk/id/eprint/49235
ISSN: 0935-1175
PURE UUID: 2b126815-a398-441e-a503-792bd1c32d69
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Date deposited: 25 Oct 2007
Last modified: 15 Mar 2024 09:54
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Author:
Alexander N. Gorban
Author:
Iliya V. Karlin
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