## Stochastic Numerics for the Boltzmann EquationStochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented. |

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### Contents

1 | |

Related Markov processes | 33 |

Stochastic weighted particle method | 65 |

Numerical experiments | 147 |

A Auxiliary results | 211 |

B Modeling of distributions 229 | 228 |

243 | |

255 | |

### Other editions - View all

Stochastic Numerics for the Boltzmann Equation Sergej Rjasanow,Wolfgang Wagner No preview available - 2005 |

Stochastic Numerics for the Boltzmann Equation Sergej Rjasanow,Wolfgang Wagner No preview available - 2009 |

Stochastic Numerics for the Boltzmann Equation Sergej Rjasanow,Wolfgang Wagner No preview available - 2010 |

### Common terms and phrases

absorption algorithms analytical assume assumptions asymptotic behavior Boltzmann equation boundary condition bounded Bscat cell chosen according collision kernel computational confidence intervals consider convergence corresponding D J R3 defined denotes density region deterministic direct simulation direction vector distribution function domain DSMC Example fictitious collision form cf free flow implies inflow interaction introduced j<ly left plot Lemma Leontovich lim sup limiting equation Mach number Markov processes max(gi Maxwell distribution Maxwellian mean free path method Monte Carlo Monte Carlo method Mott-Smith distribution Mott-Smith model Mscat notations number of particles obtains cf particle system procedure Proof qref quantities R3in random variable reduction measure Remark right plot satisfies Section shown in Fig solution spherical coordinates step stochastic SWPM Tail functional takes the form temperature test function Theorem uniformly velocity space waiting time parameter weight transfer function