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Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Clément MouhotLorenzo PareschiThomas Rey — 2013

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

Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically ( ) where is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, 339 (2004) 71–76, C. Mouhot and L. Pareschi, 75 (2006) 1833–1852], we derive fast summation techniques for the evaluation of discrete-velocity schemes which permits to...

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

Giovanni NaldiLorenzo PareschiGiuseppe Toscani — 2003

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

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...

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

Giovanni NaldiLorenzo PareschiGiuseppe Toscani — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

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...

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