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Author Bellomo, Nicola
Title Lecture Notes on the Discretization of the Boltzmann Equation
Imprint Singapore : World Scientific Publishing Co Pte Ltd, 2002
©2003
book jacket
Descript 1 online resource (317 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Series on Advances in Mathematics for Applied Sciences Ser. ; v.63
Series on Advances in Mathematics for Applied Sciences Ser
Note Intro -- CONTENTS -- Preface -- Chapter 1. From the Boltzmann Equation to Discretized Kinetic Models -- 1.1 Introduction -- 1.2 The Nonlinear Boltzmann Equation -- 1.3 The Discrete and Semicontinuous Boltzmann Equation -- 1.4 Plan of the Lecture Notes -- 1.5 References -- Chapter 2. Discrete Velocity Models for Gas Mixtures -- 2.1 Introduction -- 2.2 DVM for mixtures -- 2.3 Models with a finite number of velocities and the problem of spurious invariants -- 2.4 Constructing DVM with arbitrarily many velocities -- 2.5 Concluding remarks -- 2.6 References -- Chapter 3. Discrete Velocity Models with Multiple Collisions -- 3.1 Introduction -- 3.2 Discrete Models with Multiple Collisions -- 3.3 Macroscopic Description -- 3.4 Boundary Conditions for Discrete Models -- 3.5 Conclusion -- 3.6 References -- Chapter 4. Discretization of the Boltzmann Equation and the Semicontinuous Model -- 4.1 Introduction -- 4.2 Splitting and Energy Formulation -- 4.3 Working in a Finite Energy Interval -- 4.4 Energy Discretization and Kinetic Model -- 4.5 Conservation and Euler Equations for the Discretized Model -- 4.6 Energy Formulation of the Collision Dynamics -- 4.7 Concluding Remarks -- 4.8 References -- Chapter 5. Semi-continuous Extended Kinetic Theory -- 5.1 Introduction -- 5.2 Continuous Kinetic Equations -- 5.3 Semi-continuous Kinetic Equations -- 5.4 Treatment of the Remaining Continuous Variables -- 5.5 Relaxational Behaviour -- 5.6 Applications -- 5.7 Conclusion -- 5.8 References -- Chapter 6. Steady Kinetic Boundary Value Problems -- 6.1 Introduction -- 6.2 Discrete kinetic models -- 6.3 FEM for the semi discrete steady Boltzmann equation -- 6.4 Numerical results -- 6.5 References -- Chapter 7. Computational Methods and Fast Algorithms for Boltzmann Equations -- 7.1 Introduction -- 7.2 A one-dimensional example -- 7.3 The multi-dimensional case
7.4 References -- Chapter 8. Discrete Velocity Models and Dynamical Systems -- 8.1 Introduction -- 8.2 Statement of the Problem -- 8.3 DVM as Dynamical System -- 8.4 Linearized Equation -- 8.5 Indices of Stationary Points -- 8.6 Applications to Half-Space Problems -- 8.7 Concluding Remarks -- 8.8 References -- Chapter 9. Numerical Method for the Compton Scattering Operator -- 9.1 Introduction -- 9.2 Quantum Boltzmann and Kompaneets Equation -- 9.3 Semidiscretization -- 9.4 Time Discretization for the Kompaneets Equation -- 9.5 Numerical Tests for the Kompaneets Schemes -- 9.6 Conclusions -- 9.7 References -- Chapter 10. Discrete Models of the Boltzmann Equation in Quantum Optics and Arbitrary Partition of the Velocity Space -- 10.1 Introduction -- 10.2 Laser-induced thermal acoustics: A discrete kinetic approach -- 10.3 Modified discrete Boltzmann equation -- 10.4 Scaling of discrete velocity models -- 10.5 References -- List of Contributors
This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community. Contents: From the Boltzmann Equation to Discretized Kinetic Models (N Bellomo & R Gatignol); Discrete Velocity Models for Gas Mixtures (C Cercignani); Discrete Velocity Models with Multiple Collisions (R Gatignol); Discretization of the Boltzmann Equation and the Semicontinuous Model (L Preziosi & L Rondoni); Semi-continuous Extended Kinetic Theory (W Koller); Steady Kinetic Boundary Value Problems (H Babovsky et al.); Computational Methods and Fast Algorithms for the Boltzmann Equation (L Pareschi); Discrete Velocity Models and Dynamical Systems (A Bobylev & N Bernhoff); Numerical Method for the Compton Scattering Operator (C Buet & S Cordier); Discrete Models of the Boltzmann Equation in Quantum Optics and Arbitrary Partition of the Velocity Space (F Schürrer). Readership: Higher level postgraduates in applied mathematics
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Bellomo, Nicola Lecture Notes on the Discretization of the Boltzmann Equation Singapore : World Scientific Publishing Co Pte Ltd,c2002 9789812382252
Subject Transport theory.;Finite element method.;Differential equations -- Asymptotic theory
Electronic books
Alt Author Gatignol, Renée
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