Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
Department of Mathematics and Applications, University of
Milano-Bicocca, Milano, Italy. email@example.com.
2 Department of Mathematics, University of Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy. firstname.lastname@example.org.
3 Department of Mathematics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy. email@example.com.
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.
Mathematics Subject Classification: 65L60 / 65R20 / 76P05 / 82C40
Key words: Boltzmann equation / granular media / spectral methods / singular integrals / nonlinear friction equation / quasi elastic limit.
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