Modeling and Computational Methods for Kinetic Equations

Front Cover
Pierre Degond, Lorenzo Pareschi, Giovanni Russo
Springer Science & Business Media, Dec 6, 2012 - Mathematics - 356 pages

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods.

This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused theoretical or applied works.

The book is divided into two parts. Part I is devoted to the most fundamental kinetic model: the Boltzmann equation of rarefied gas dynamics. Additionally, widely used numerical methods for the discretization of the Boltzmann equation are reviewed: the Monte--Carlo method, spectral methods, and finite-difference methods. Part II considers specific applications: plasma kinetic modeling using the Landau--Fokker--Planck equations, traffic flow modeling, granular media modeling, quantum kinetic modeling, and coagulation-fragmentation problems.

Modeling and Computational Methods of Kinetic Equations will be accessible to readers working in different communities where kinetic theory is important: graduate students, researchers and practitioners in mathematical physics, applied mathematics, and various branches of engineering. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.

 

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Contents

a review
3
global existence results
59
Chapter 3 MonteCarlo methods for the Boltzmann equation
81
Chapter 4 Accurate numerical methods for the Boltzmann equation
116
Chapter 5 Finitedifference methods for the Boltzmann equation for binary gas mixtures
147
Part II Applications
168
the FokkerPlanckLandau equation
171
Chapter 7 On multipole approximations of the FokkerPlanckLandau operator
194
models and numerics
219
Chapter 9 Modelling and numerical methods for granular gases
259
modelling and numerics for BoseEinstein condensation
287
Chapter 11 On coalescence equations and related models
321
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