Ebook: Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows

This book is concerned with the methods of solving the nonlinear Boltz­ mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi­ librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in­ vestigated for the first time. The structure and the contents of the present book have some com­ mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.

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The outstanding points of our book consist of investigations into the possibility of the numerical schemes of the direct method for solving the Boltzmann equation. Both deterministic and Monte Carlo procedures are considered to evaluate the collision integrals. The main mathematical tool is the conservative splitting method on the basis of which, a set of classical and new problems are solved to study nonequilibrium gas flows. This monograph differs from other books in the same field, because, for example the book by G.A. Bird is concerned with the approach of simulation of rarefied gas flows and the book by C. Cercignani deals with the classical kinetic theory issues and describes mainly the analytical and engineering methods for solving the Boltzmann equation. Our book is the first (as we know) monograph which is devoted to the numerical direct solving of the Boltzmann equation. The intended level of readership are graduate and postgraduate students and researches. This book can be used by the target groups as the mathematical apparatus to numerical study of complex problems of nonequilibrium gas flows.

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The outstanding points of our book consist of investigations into the possibility of the numerical schemes of the direct method for solving the Boltzmann equation. Both deterministic and Monte Carlo procedures are considered to evaluate the collision integrals. The main mathematical tool is the conservative splitting method on the basis of which, a set of classical and new problems are solved to study nonequilibrium gas flows. This monograph differs from other books in the same field, because, for example the book by G.A. Bird is concerned with the approach of simulation of rarefied gas flows and the book by C. Cercignani deals with the classical kinetic theory issues and describes mainly the analytical and engineering methods for solving the Boltzmann equation. Our book is the first (as we know) monograph which is devoted to the numerical direct solving of the Boltzmann equation. The intended level of readership are graduate and postgraduate students and researches. This book can be used by the target groups as the mathematical apparatus to numerical study of complex problems of nonequilibrium gas flows.
Content:
Front Matter....Pages i-xvii
The Boltzmann Equation as a Physical and Mathematical Model....Pages 1-21
Survey of Mathematical Approaches to Solving the Boltzmann Equation....Pages 23-43
Main Features of the Direct Numerical Approaches....Pages 45-68
Deterministic (Regular) Method for Solving the Boltzmann Equation....Pages 69-83
Construction of Conservative Scheme for the Kinetic Equation....Pages 85-108
Parallel Algorithms for the Kinetic Equation....Pages 109-119
Application of the Conservative Splitting Method for Investigating Near Continuum Gas Flows....Pages 121-138
Study of Uniform Relaxation in Kinetic Gas Theory....Pages 139-154
Nonuniform Relaxation Problem as a Basic Model for Description of Open Systems....Pages 155-179
One-Dimensional Kinetic Problems....Pages 181-209
Multi-Dimensional Problems. Study of Free Jet Flows....Pages 211-225
The Boltzmann Equation and the Description of Unstable Flows....Pages 227-239
Solutions of Some Multi-Dimensional Problems....Pages 241-270
Special Hypersonic Flows and Flows with Very High Temperatures....Pages 271-294
Back Matter....Pages 295-302

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The outstanding points of our book consist of investigations into the possibility of the numerical schemes of the direct method for solving the Boltzmann equation. Both deterministic and Monte Carlo procedures are considered to evaluate the collision integrals. The main mathematical tool is the conservative splitting method on the basis of which, a set of classical and new problems are solved to study nonequilibrium gas flows. This monograph differs from other books in the same field, because, for example the book by G.A. Bird is concerned with the approach of simulation of rarefied gas flows and the book by C. Cercignani deals with the classical kinetic theory issues and describes mainly the analytical and engineering methods for solving the Boltzmann equation. Our book is the first (as we know) monograph which is devoted to the numerical direct solving of the Boltzmann equation. The intended level of readership are graduate and postgraduate students and researches. This book can be used by the target groups as the mathematical apparatus to numerical study of complex problems of nonequilibrium gas flows.
Content:
Front Matter....Pages i-xvii
The Boltzmann Equation as a Physical and Mathematical Model....Pages 1-21
Survey of Mathematical Approaches to Solving the Boltzmann Equation....Pages 23-43
Main Features of the Direct Numerical Approaches....Pages 45-68
Deterministic (Regular) Method for Solving the Boltzmann Equation....Pages 69-83
Construction of Conservative Scheme for the Kinetic Equation....Pages 85-108
Parallel Algorithms for the Kinetic Equation....Pages 109-119
Application of the Conservative Splitting Method for Investigating Near Continuum Gas Flows....Pages 121-138
Study of Uniform Relaxation in Kinetic Gas Theory....Pages 139-154
Nonuniform Relaxation Problem as a Basic Model for Description of Open Systems....Pages 155-179
One-Dimensional Kinetic Problems....Pages 181-209
Multi-Dimensional Problems. Study of Free Jet Flows....Pages 211-225
The Boltzmann Equation and the Description of Unstable Flows....Pages 227-239
Solutions of Some Multi-Dimensional Problems....Pages 241-270
Special Hypersonic Flows and Flows with Very High Temperatures....Pages 271-294
Back Matter....Pages 295-302
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