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

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

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## Abstract

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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 [CITE] 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.

## How to cite

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Naldi, 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 37.1 (2010): 73-90. <http://eudml.org/doc/194157>.

@article{Naldi2010,
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 [CITE] 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},
keywords = {Boltzmann equation; granular media; spectral methods; singular integrals; nonlinear friction equation; quasi elastic limit.; Fourier method; nonlinear friction equation},
language = {eng},
month = {3},
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/194157},
volume = {37},
year = {2010},
}

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
DA - 2010/3//
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 [CITE] 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; nonlinear friction equation
UR - http://eudml.org/doc/194157
ER -

## References

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