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Spectral methods for one-dimensional kinetic modelsofgranular flows and numerical quasi elastic limit

Published online by Cambridge University Press:  15 March 2003

Giovanni Naldi ,
Lorenzo Pareschi  and
Giuseppe Toscani
Giovanni Naldi
Affiliation:
Department of Mathematics and Applications, University of Milano-Bicocca, Milano, Italy. naldi@matapp.unimib.it.
Lorenzo Pareschi
Affiliation:
Department of Mathematics, University of Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy. pareschi@dm.unife.it.
Giuseppe Toscani
Affiliation:
Department of Mathematics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy. toscani@dimat.unipv.it.
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Abstract

In this paper we introduce numerical schemes for aone-dimensional kinetic model of the Boltzmann equation withdissipative collisions and variable coefficient of restitution. Inparticular, we study the numerical passage of the Boltzmannequation with singular kernel to nonlinear friction equations inthe so-called quasi elastic limit. To this aim we introduce aFourier spectral method for the Boltzmann equation [CITE]and show that the kernel modes that define the spectral methodhave the correct quasi elastic limit providing a consistentspectral method for the limiting nonlinear friction equation.

Keywords

Boltzmann equationgranular mediaspectral methodssingular integralsnonlinearfriction equationquasi elastic limit.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 1 , January 2003 , pp. 73 - 90
Copyright
© EDP Sciences, SMAI, 2003

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