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Kinetic theory and fluid dynamics. (English) Zbl 1021.76002
Modeling and Simulation in Science, Engineering and Technology. Basel: Birkhäuser. xii, 353 p. EUR 99.00/net; sFr. 156.00 (2002).
This monograph is a comprehensive description of the relationships between kinetic theory and fluid dynamics, mainly for a time-independent problem in a general domain. Ambiguities are classified, and the incompleteness of classical fluid dynamics in describing the gas behaviour in the continuum limit is discussed. By a systematic asymptotic analysis, fluid dynamics-type equations and their boundary conditions which take into account the effect of gas rarefaction are derived from the Boltzmann system. Comprehensive information on the Knudsen-Payer correction is given, and equations as well as their boundary conditions are classified depending on the physical context of the problems. Applications are presented for flows induced by temperature fields, for evaporation and condensation problems, for ghost effects, and for bifurcation of flows.

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76A02 Foundations of fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics