LORENZO PARESCHI and GIOVANNI RUSSO
An introduction to the numerical analysis of the Boltzmann equation
Received: 13 July 2005 Revised: 3 October 2005
Mathematics Subject Classification (2000): 65C05 - 65L60 - 65R20 - 76P05 82C40
Abstract: The different aspects of the numerical solution of the Boltzmann equation and related kinetic models are analyzed and discussed both from a deterministic as well as from a probabilistic view- point. In both settings after a review of classical methods like discrete velocity modelling and direct simulation Monte Carlo, the emphasis is addressed to the most recent developments in the field, such as (fast) spectral methods and time relaxed Monte Carlo methods. Besides the algorithmic aspects and the efficiency of the methods, considerations on stability, accuracy and consistency of the various schemes are reported.