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The Lattice Boltzmann EquationFor Complex States of Flowing Matter$
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Sauro Succi

Print publication date: 2018

Print ISBN-13: 9780199592357

Published to Oxford Scholarship Online: June 2018

DOI: 10.1093/oso/9780199592357.001.0001

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Model Boltzmann Equations

Model Boltzmann Equations

(p.125) 8 Model Boltzmann Equations
The Lattice Boltzmann Equation

Sauro Succi

Oxford University Press

This chapter deals with simplified models of the Boltzmann equation, aimed at reducing its mathematical complexity, while still retaining the most salient physical features. As observed many times in this book, the Boltzmann equation is all but an easy equation to solve. The situation surely improves by moving to its linearized version, but even then, a lot of painstaking labor is usually involved in deriving special solutions for the problem at hand. In order to ease this state of affairs, in the mid-fifties, stylized models of the Boltzmann equations were formulated, with the main intent of providing facilitated access to the main qualitative aspects of the actual solutions of the Boltzmann equation, without facing head-on with its mathematical complexity. As it is always the case with models, the art is not to throw away the baby with the tub water.

Keywords:   model equations, approximations, mathematical complexity, stylized models, qualitative aspects, facilitated access

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