Modeling and Computational Methods for Kinetic Equations

by Degond, Pierre; Pareschi, Lorenzo; Russo, Giovanni

• ISBN13: 9780817632540
• ISBN10: 0817632549
• Format: Hardcover
• Copyright: 2004-06-01
• Publisher: Birkhauser

Summary

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.

Table of Contents

Preface	vii
Part I Rarefied Gases
1. Macroscopic limits of the Boltzmann equation: a review
Pierre Degond	3	(56)
2. Moment equations for charged particles: global existence results
Giuseppe Ali, Angelo Marcello Anile	59	(22)
3. Monte-Carlo methods for the Boltzmann equation
Sergej Rjasanow	81	(36)
4. Accurate numerical methods for the Boltzmann equation
Francis Filbet, Giovanni Russo	117	(30)
5. Finite-difference methods for the Boltzmann equation for binary gas mixtures
Kazuo Aoki, Shingo Kosuge	147	(24)
Part II Applications
6. Plasma kinetic models: the Fokker-Planck-Landau equation
Laurent Desvillettes	171	(24)
7. On multipole approximations of the Fokker-Planck-Landau operator
Mohammed Lemou	195	(24)
8. Traffic flow: models and numerics
Axel Klar, Raimund Wegener	219	(40)
9. Modelling and numerical methods for granular gases
Lorenzo Pareschi, Giuseppe Toscani	259	(28)
10. Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation
Weizhu Bao, Lorenzo Pareschi, Peter A. Markowich	287	(34)
11. On coalescence equations and related models
Philippe Laurencot, Stéphane Mischler	321