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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).

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: 17 Jul 2017 14:56

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Contributors

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

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