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

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
0935-1175
311-335
Gorban, Alexander N.
31914661-757a-4b6b-a953-109ac7499746
Karlin, Iliya V.
3331716f-692a-4b81-87a4-9aad489d025d
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), 311-335. (doi:10.1007/s00161-005-0202-z).

Record type: Article

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: 08 Jan 2022 03:59

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Contributors

Author: Alexander N. Gorban
Author: Iliya V. Karlin

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