Lecture notes on the discretization of the Boltzmann equation / editors Nicola Bellomo, Renee Gatignol.

Format:

Book

Contributor:

Bellomo, N.

Gatignol, Renée.

Series:

Series on advances in mathematics for applied sciences ; v. 63.

Series on advances in mathematics for applied sciences ; v. 63

Language:

English

Subjects (All):

Transport theory.

Finite element method.

Differential equations--Asymptotic theory.

Differential equations.

Physical Description:

1 online resource (317 p.)

Edition:

1st ed.

Place of Publication:

River Edge, NJ : World Scientific, c2003.

Language Note:

English

Summary:

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. <br><i>Contents:</i><ul><li>From the Boltzmann Equation to Discretized Kinetic Models <i>(N Bellomo & R Gatignol)</i>

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611947927

9781281947925

128194792X

9789812796905

9812796908

OCLC:

879023694