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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.

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

Preface. Introduction. 1. The Boltzmann Equation as a Physical and Mathematical Model. 2. Survey of Mathematical Approaches to Solving the Boltzmann Equation. 3. Main Features of the Direct Numerical Approaches. 4. Deterministic (Regular) Method for Solving the Boltzmann Equation. 5. Construction of Conservative Scheme for the Kinetic Equation. 6. Parallel Algorithms for the Kinetic Equation. 7. Application of the Conservative Splitting Method for Investigating Near Continuum Gas Flows. 8. Study of Uniform Relaxation in Kinetic Gas Theory. 9. Nonuniform Relaxation Problem as a Basic Model for Description of Open Systems. 10. One-Dimensional Kinetic Problems. 11. Multi-Dimensional Problems. Study of Free Jet Flows. 12. The Boltzmann Equation and the Description of Unstable Flows. 13. Solutions of Some Multi-Dimensional Problems. 14. Special Hypersonic Flows and Flows with Very High Temperatures.