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

  • Book
  • © 2001

Overview

Authors:
  1. V. V. Aristov

    1. Computing Center of the Russian Academy of Sciences, Moscow, Russia

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Part of the book series: Fluid Mechanics and Its Applications (FMIA, volume 60)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xvii
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  2. The Boltzmann Equation as a Physical and Mathematical Model

    • V. V. Aristov
    Pages 1-21

  3. Survey of Mathematical Approaches to Solving the Boltzmann Equation

    • V. V. Aristov
    Pages 23-43

  4. Main Features of the Direct Numerical Approaches

    • V. V. Aristov
    Pages 45-68

  5. Deterministic (Regular) Method for Solving the Boltzmann Equation

    • V. V. Aristov
    Pages 69-83

  6. Construction of Conservative Scheme for the Kinetic Equation

    • V. V. Aristov
    Pages 85-108

  7. Parallel Algorithms for the Kinetic Equation

    • V. V. Aristov
    Pages 109-119

  8. Application of the Conservative Splitting Method for Investigating Near Continuum Gas Flows

    • V. V. Aristov
    Pages 121-138

  9. Study of Uniform Relaxation in Kinetic Gas Theory

    • V. V. Aristov
    Pages 139-154

  10. Nonuniform Relaxation Problem as a Basic Model for Description of Open Systems

    • V. V. Aristov
    Pages 155-179

  11. One-Dimensional Kinetic Problems

    • V. V. Aristov
    Pages 181-209

  12. Multi-Dimensional Problems. Study of Free Jet Flows

    • V. V. Aristov
    Pages 211-225

  13. The Boltzmann Equation and the Description of Unstable Flows

    • V. V. Aristov
    Pages 227-239

  14. Solutions of Some Multi-Dimensional Problems

    • V. V. Aristov
    Pages 241-270

  15. Special Hypersonic Flows and Flows with Very High Temperatures

    • V. V. Aristov
    Pages 271-294

  16. Back Matter

    Pages 295-302
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Keywords

About this book

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.

Authors and Affiliations

  • Computing Center of the Russian Academy of Sciences, Moscow, Russia

    V. V. Aristov

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