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050  4 QC718.5.T7L43 2003 
082 0  530.13 
100 1  Bellomo, Nicola 
245 10 Lecture Notes on the Discretization of the Boltzmann 
       Equation 
264  1 Singapore :|bWorld Scientific Publishing Co Pte Ltd,|c2002
264  4 |c©2003 
300    1 online resource (317 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
490 1  Series on Advances in Mathematics for Applied Sciences 
       Ser. ;|vv.63 
505 0  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 
505 8  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
520    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 
588    Description based on publisher supplied metadata and other
       sources 
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
       may be limited to ProQuest Ebook Central affiliated 
       libraries 
650  0 Transport theory.;Finite element method.;Differential 
       equations -- Asymptotic theory 
655  4 Electronic books 
700 1  Gatignol, Renée 
776 08 |iPrint version:|aBellomo, Nicola|tLecture Notes on the 
       Discretization of the Boltzmann Equation|dSingapore : 
       World Scientific Publishing Co Pte Ltd,c2002
       |z9789812382252 
830  0 Series on Advances in Mathematics for Applied Sciences Ser
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