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Kinetic Theory and Transport Phenomena$
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Rodrigo Soto

Print publication date: 2016

Print ISBN-13: 9780198716051

Published to Oxford Scholarship Online: June 2016

DOI: 10.1093/acprof:oso/9780198716051.001.0001

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Numerical and semianalytical methods

Numerical and semianalytical methods

(p.209) 10 Numerical and semianalytical methods
Kinetic Theory and Transport Phenomena

Rodrigo Soto

Oxford University Press

Kinetic equations become extremely complex when models become realistic for several effects taking place simultaneously. It is hopeless trying to find analytic solutions and numerical methods should therefore be devised to solve them. This chapter presents numerical methods appropriate for kinetic theory. First, the moment method is described, where the kinetic equations are transformed into coupled partial differential equations, which can be solved using standard tools. The method is exemplified by the Grad method for the Boltzmann equation. Second, the stochastic methods are presented, where particles sample the distribution function and are advanced in time so as to reproduce the evolution of the distribution function. Special methods are given to reproduce the streaming motion, particle collisions (classical and quantum), Brownian motion, and long-range interactions.

Keywords:   moment method, Grad method, reproduce particle collisions, Brownian motion, long-range interactions

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