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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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.
|Digital Object Identifier (DOI):||doi:10.1007/s00161-005-0202-z|
|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
|Accepted Date and Publication Date:||
|Date Deposited:||25 Oct 2007|
|Last Modified:||31 Mar 2016 12:26|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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