Synopses & Reviews
This monograph gives a comprehensive description of the relationship and connections between kinetic theory and fluid dynamics, mainly for a time-independent problem in a general domain. Ambiguities in this relationship are clarified, and the incompleteness of classical fluid dynamics in describing the behavior of a gas in the continuum limit--recently reported as the ghost effect--is also discussed. The approach used in this work engages an audience of theoretical physicists, applied mathematicians, and engineers. By a systematic asymptotic analysis, fluid-dynamic-type equations and their associated boundary conditions that take into account the weak effect of gas rarefaction are derived from the Boltzmann system. Comprehensive information on the Knudsen-layer correction is also obtained. Equations and their boundary conditions are carefully classified depending on the physical context of problems. Applications are presented to various physically interesting phenomena, including flows induced by temperature fields, evaporation and condensation problems, examples of the ghost effect, and bifurcation of flows. Key features: * many applications and physical models of practical interest * experimental works such as the Knudsen compressor are examined to supplement theory * engineers will not be overwhelmed by sophisticated mathematical techniques * mathematicians will benefit from clarity of definitions and precise physical descriptions given in mathematical terms * appendices collect key derivations and formulas, important to the practitioner, but not easily found in the literature Kinetic Theory and Fluid Dynamics serves as a bridge for those working in different communities where kinetic theory or fluid dynamics is important: graduate students, researchers and practitioners in theoretical physics, applied mathematics, and various branches of engineering. The work can be used in graduate-level courses in fluid dynamics, gas dynamics, and kinetic theory; some parts of the text can be used in advanced undergraduate courses.
Review
"Yoshio Sone is certainly one of the world leading experts for continuum limits of the Boltzmann equation and with this book he summarizes the extensive work of his group on this subject. The text is very carefully written and even if the expansions and equations are lengthy, the results are always interpreted and discussed.
Table of Contents
Preface Introduction Boltzmann Equation Linear Theory---Small Reynolds Numbers Weakly Nonlinear Theory---Finite Reynolds Numbers Nonlinear Theory I---Finite Temperature Variations and Ghost Effect Nonlinear Theory II---Flow with a Finite Mach Number around a Simple Boundary Nonlinear Theory III---Finite Speed of Evaporation and Condensation Bifurcation of Cylindrical Couette Flow with Evaporation and Condensation Appendix A: Supplementary Explanations and Formulas Appendix B: Spherically Symmetric Field of Symmetric Tensor Appendix C: Kinetic-Equation Approach to Fluid-Dynamic Equations Bibliography Index