Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Conservative energy discretization of Boltzmann collision operator

Authors: L. Preziosi and L. Rondoni
Journal: Quart. Appl. Math. 57 (1999), 699-721
MSC: Primary 76P05; Secondary 82C40
DOI: https://doi.org/10.1090/qam/1724301
MathSciNet review: MR1724301
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Abstract: The paper deduces a kinetic model obtained introducing a discretization of the Boltzmann equation based on an equispaced distribution of allowed particle energies. The model obtained is a system of integro-differential equations with integration over suitable angular variables: one over the portion of the unit sphere between two parallels symmetric with respect to the equatorial plane perpendicular to the velocity of the field particle, and one over a unit circle. The model preserves mass, momentum and energy. Furthermore, there exists an $ H$-functional describing trend toward an equilibrium state described by a Gaussian distribution. Particular attention is paid to the identification of a criterion which indicates the values of the discretization parameters.

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DOI: https://doi.org/10.1090/qam/1724301
Article copyright: © Copyright 1999 American Mathematical Society

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