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, Volume 37 (2003) no. 1, p. 73-90

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.

DOI : https://doi.org/10.1051/m2an:2003019
Classification:  65L60,  65R20,  76P05,  82C40
Keywords: Boltzmann equation, granular media, spectral methods, singular integrals, nonlinear friction equation, quasi elastic limit
     author = {Naldi, Giovanni and Pareschi, Lorenzo and Toscani, Giuseppe},
     title = {Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {1},
     year = {2003},
     pages = {73-90},
     doi = {10.1051/m2an:2003019},
     zbl = {1046.76034},
     mrnumber = {1972651},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2003__37_1_73_0}
Naldi, Giovanni; Pareschi, Lorenzo; 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, Volume 37 (2003) no. 1, pp. 73-90. doi : 10.1051/m2an:2003019. http://www.numdam.org/item/M2AN_2003__37_1_73_0/

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