Boltzmann Equation -- Highly Rarefied Gas: Free Molecular Gas and Its Correction -- Slightly Rarefied Gas: Asymptotic Theory of the Boltzmann System for Small Knudsen Numbers -- Simple Flows -- Flows Induced by Temperature Fields -- Flows with Evaporation and Condensation -- Bifurcation in the Half-Space Problem of Evaporation and Condensation -- Ghost Effect and Bifurcation I: Bénard and Taylor-Couette Problems -- Ghost Effect and Bifurcation II: Ghost Effect of Infinitesimal Curvature and Bifurcation of the Plane Couette Flow.

This self-contained work is an up-to-date treatment of the basic theory of molecular gas dynamics and its various applications. Recent progress in the field has greatly enhanced the original theory and stimulated interesting and critical gas dynamic phenomena and problems. This book, unique in the literature, presents working knowledge, theory, techniques, and typical phenomena in rarefied gases for theoretical development and applications. Basic theory is developed in a systematic way and presented in a form easily applied to practical use. After presenting basic theory and various simple flows, such as unidirectional or quasi-unidirectional flows and flows around a sphere, the author discusses additional topics, including flows induced by temperature fields, which are typical in rarefied gases; flows with evaporation and condensation; and bifurcation of flows in rarefied gases. The appendix contains many useful fundamental formulae, as well as an explanation of the theoretical background for the direct simulation Monte Carlo (DSMC) method, easily accessible to nonmathematicians and not found elsewhere in the literature. Existence of the ghost effect has made molecular gas dynamics indispensable to the study of a gas in the continuum limit, traditionally treated by classical fluid dynamics. In this book, the ghost and non-Navier–Stokes effects are demonstrated for typical examples—such as Bénard and Taylor–Couette problems—in the context of a new framework. An infinitesimal curvature effect is also discussed, with a long-standing problem of the bifurcation of the plane Couette flow worked out as an example. Molecular Gas Dynamics is useful 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 may be used as a self-study reference or as a textbook in graduate-level courses on fluid dynamics, gas dynamics, kinetic theory, molecular or rarefied gas dynamics, microflows, and applied mathematics.

9780817645731

10.1007/978-0-8176-4573-1 doi

Physics.

Applied mathematics.

Engineering mathematics.

Mathematical models.

Fluids.

Physics.

Physics, general.

Applications of Mathematics.

Theoretical, Mathematical and Computational Physics.

Mathematical Modeling and Industrial Mathematics.

Mathematical Methods in Physics.

Fluid- and Aerodynamics.

QC1-75

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