## Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium FlowsThis 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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### Contents

IV | 1 |

V | 6 |

VI | 10 |

VII | 13 |

VIII | 21 |

IX | 23 |

X | 25 |

XI | 27 |

XLIII | 139 |

XLIV | 140 |

XLV | 146 |

XLVI | 148 |

153 | |

XLVIII | 155 |

XLIX | 159 |

L | 164 |

XII | 29 |

XIII | 30 |

XIV | 31 |

XV | 33 |

XVI | 39 |

XVII | 45 |

XVIII | 49 |

XIX | 51 |

XX | 56 |

XXI | 58 |

XXII | 61 |

XXIII | 67 |

XXIV | 69 |

XXV | 70 |

XXVI | 75 |

XXVII | 77 |

83 | |

XXIX | 85 |

XXX | 87 |

XXXI | 93 |

XXXII | 98 |

XXXIII | 103 |

XXXIV | 107 |

XXXV | 109 |

XXXVI | 111 |

XXXVII | 113 |

XXXVIII | 119 |

XXXIX | 121 |

XL | 124 |

XLI | 131 |

XLII | 137 |

### Other editions - View all

Direct Methods for Solving the Boltzmann Equation and Study of ... V.V. Aristov Limited preview - 2001 |

Direct Methods for Solving the Boltzmann Equation and Study of ... V.V. Aristov Limited preview - 2012 |

Direct Methods for Solving the Boltzmann Equation and Study of ... V.V. Aristov No preview available - 2012 |

### Common terms and phrases

accuracy algorithm approach approximation Aristov V.V. Boltzmann equation boundary conditions calculations cell Chapter coefficients collision integrals comparison component conservation laws conservative splitting method considered contour lines coordinates direct integration direct numerical direct simulation discrete velocity distribution function DSMC entropy equilibrium error Figure finite Fluids formula free jet free-molecular gas flows grid heat flux implicit scheme ISBN iterations IUTAM Symposium held jet flows kinetic equation kinetic theory Mach number Math mathematical Maxwellian mean free path mean velocity molecular Monte Carlo method Navier-Stokes equations nonequilibrium nonlinear nonuniform relaxation number of nodes numerical analysis numerical schemes numerical solutions obtained one-dimensional problem orifice parallel parallel computing particles Phys physical space processors Rarefied Gas Dynamics relaxation problem relaxation stage right-hand side shock wave shock wave structure small Knudsen numbers solving the Boltzmann spatial Tcheremissine F.G. temperature three-dimensional tion turbulent uniform relaxation USSR values velocity space zero