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. Semicontinuous Extended Kinetic Theory  5.1 Introduction  5.2 Continuous Kinetic Equations  5.3 Semicontinuous 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 onedimensional example  7.3 The multidimensional 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 HalfSpace 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 Laserinduced 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); Semicontinuous 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, RenÃ©e

