On the fast evaluation of kinetic equations for driven granular flows
Spectral methods based on Fourier series have been recently introduced for the Boltzmann [6, 7] and Landau  integral operators. These spectral schemes allow us to obtain spectrally accurate solutions with a reduction of the computational cost strictly related to the particular structure of the integral. A reduction from N 2 to N log2 N is readily deducible for the Landau equation, whereas in the Boltzmann case such a reduction does not seem possible. Here we extend the spectral method to the case of the Boltzmann collision integral for one dimensional granular media and discuss the possibility of developing approximate methods that bring the overall computational cost to N log2 N.
KeywordsBoltzmann Equation Spectral Method Granular Medium Granular Flow Collision Operator
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