Moment closure approximations of the Boltzmann equation based on φ-divergences

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This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to (Formula presented.)-divergences and a corresponding closure procedure based on minimization of (Formula presented.)-divergences. The proposed description encapsulates as special cases Grad’s classical closure based on expansion in Hermite polynomials and Levermore’s entropy-based closure. We establish that the generalization to divergence-based closures enables the construction of extended thermodynamic theories that avoid essential limitations of the standard moment-closure formulations such as inadmissibility of the approximate phase-space distribution, potential loss of hyperbolicity and singularity of flux functions at local equilibrium. The divergence-based closure leads to a hierarchy of tractable symmetric hyperbolic systems that retain the fundamental structural properties of the Boltzmann equation.

Originele taal-2Engels
Pagina's (van-tot)77-104
Aantal pagina's28
TijdschriftJournal of Statistical Physics
Volume164
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - jul 2016

Vingerafdruk

Moment Closure
Boltzmann Equation
closures
Divergence
divergence
Closure
moments
Approximation
approximation
Inadmissibility
Symmetric Hyperbolic Systems
Local Equilibrium
Relative Entropy
Hermite Polynomials
Hyperbolicity
Method of Moments
entropy
hyperbolic systems
Structural Properties
Phase Space

Citeer dit

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Moment closure approximations of the Boltzmann equation based on φ-divergences. / Abdel Malik, M.; van Brummelen, E.H.

In: Journal of Statistical Physics, Vol. 164, Nr. 1, 07.2016, blz. 77-104.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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