# Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit

Giovanni Naldi; Lorenzo Pareschi; Giuseppe Toscani

- Volume: 37, Issue: 1, page 73-90
- ISSN: 0764-583X

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topNaldi, Giovanni, Pareschi, Lorenzo, and Toscani, Giuseppe. "Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.1 (2003): 73-90. <http://eudml.org/doc/244762>.

@article{Naldi2003,

abstract = {In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [25, 26] and show that the kernel modes that define the spectral method have the correct quasi elastic limit providing a consistent spectral method for the limiting nonlinear friction equation.},

author = {Naldi, Giovanni, Pareschi, Lorenzo, Toscani, Giuseppe},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Boltzmann equation; granular media; spectral methods; singular integrals; nonlinear friction equation; quasi elastic limit; Fourier method},

language = {eng},

number = {1},

pages = {73-90},

publisher = {EDP-Sciences},

title = {Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit},

url = {http://eudml.org/doc/244762},

volume = {37},

year = {2003},

}

TY - JOUR

AU - Naldi, Giovanni

AU - Pareschi, Lorenzo

AU - Toscani, Giuseppe

TI - Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2003

PB - EDP-Sciences

VL - 37

IS - 1

SP - 73

EP - 90

AB - In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [25, 26] and show that the kernel modes that define the spectral method have the correct quasi elastic limit providing a consistent spectral method for the limiting nonlinear friction equation.

LA - eng

KW - Boltzmann equation; granular media; spectral methods; singular integrals; nonlinear friction equation; quasi elastic limit; Fourier method

UR - http://eudml.org/doc/244762

ER -

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