Stochastic Numerics for the Boltzmann Equation

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Springer Science & Business Media, Mar 30, 2006 - Mathematics - 256 pages
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Stochastic 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

Kinetic theory
1
Related Markov processes
33
Stochastic weighted particle method
65
Numerical experiments
147
A Auxiliary results
211
B Modeling of distributions 229
228
References
243
Index
255
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About the author (2006)

Wolfgang Wagner is Professor of Thermodynamics at the Ruhr-University Bochum in the position of a chair. His efforts in the scientific working field cover the thermophysical properties of fluids (gases and liquids), in particular the multiparameter equations of state and highly-accurate density measurements over large ranges of temperature, pressure, and density. His research works have resulted in more than 150 publications including three books.
Prof. Wagner is an active member of the International Association of the Properties of Water and Steam (IAPWS). Under his supervision, the "IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use" (IAPWS-95) and the "IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam" (IAPWS-IF97) were developed.
In 1998 he received the Honorary Fellow Award of IAPWS and in 2003 the Yeram S. Touloukian Award of the American Society of Mechanical Engineers (ASME) for outstanding technical contributions in the field of thermophysical properties.

Hans-Joachim Kretzschmar is Professor of Technical Thermodynamics at the Zittau/ Goerlitz University of Applied Sciences and specializes in the calculation of the properties for working fluids in heat cycles, boilers, and turbines. The property libraries for water and steam, humid air, and humid combustion gases developed by his group are used worldwide in more than 140 companies, universities, and other institutions.
Prof. Kretzschmar is an active member of the International Association for the Properties of Water and Steam (IAPWS) and Vice Chairman of the IAPWS Working Group on "Thermophysical Propertiesof Water and Steam" (TPWS). As such, he was involved in the development of the industrial standard IAPWS-IF97.
As chairman of the Task Group on "Supplementary Backward Equations for the Industrial Formulation IAPWS-IF97" he has coordinated the development of further backward equations for thermodynamic process modelling. His research group in Zittau developed the supplementary standards IAPWS-IF97-S01, -S03 and -S04.