| Description |
1 online resource |
| Contents |
Cover; Preface; Acknowledgements; Contents; Part I Kinetic Theory of Fluids; 1 Why a Kinetic Theory of Fluids?; 1.1 The Navier-Stokes Equation; 1.1.1 Elementary Derivation of the Navier-Stokes Equations; 1.1.2 Navier-Stokes Equations in Lagrangian Form; 1.1.3 Navier-Stokes Equations in Coordinate Form; 1.2 Computational Aspects of the Navier-Stokes Equations; 1.2.1 Why Is the Reynolds Number so Large?; 1.3 The Benefits of Kinetic Extra Dimensions; 1.3.1 Molecular Streaming versus Fluid Advection; 1.3.2 Molecular Relaxation versus Momentum Diffusivity; 1.4 Summary; References; Exercises |
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2 Boltzmann's Kinetic Theory2.1 Atomistic Dynamics; 2.2 Statistical Dynamics: Boltzmann and the BBGKY Hierarchy; 2.3 The Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) Hierarchy; 2.4 Back to Boltzmann; 2.4.1 Two-Body Scattering; 2.4.2 Spatial Ordering in Dilute Gases; 2.4.3 Two-Body Scattering Problem; 2.4.4 Distinguished Potentials; 2.4.5 Molecular Chaos (Stosszahlansatz); 2.5 Local and Global Equilibria; 2.5.1 Local Equilibria and Equation of State; 2.5.2 The Evershifting Battle; 2.6 Summary; References; Exercises; 3 Approach to Equilibrium, the H-Theorem and Irreversibility |
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3.1 Approach to Equilibrium: the Second Principle of Thermodynamics3.2 Approach to Equilibrium, the H-Theorem; 3.2.1 Sketch of the Proof of the H-Theorem; 3.2.2 H-theorem and Irreversibility; 3.3 Collisionless Vlasov Equilibria; 3.4 The Boltzmann Equation in Modern Mathematics; 3.5 Summary; References; Exercises; 4 Transport Phenomena; 4.1 Length Scales and Transport Phenomena; 4.2 Mean-Free Path (Again!); 4.3 Transport Parameters: Macroscopic Picture; 4.3.1 Mass Diffusivity; 4.3.2 Momentum Diffusivity: Kinematic Viscosity; 4.3.3 Energy Diffusivity: Thermal Conductivity |
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4.4 Transport Parameters: Kinetic Picture4.4.1 The Structure of Dissipation: Micro versus Macro; 4.5 Dimensionless Numbers; 4.6 Beyond Fick's Law: Non-Local and Nonlinear Transport; 4.7 Summary; References; Exercises; 5 From Kinetic Theory to Navier-Stokes Hydrodynamics; 5.1 From Kinetic Theory to Hydrodynamics: Heuristic Derivation; 5.1.1 Moment Balance Equations; 5.1.2 Closures: the Enslaving Principle; 5.2 The Hilbert expansion; 5.3 Beyond Hilbert: the Chapman-Enskog Multiscale Expansion; 5.3.1 Higher-Order Hydrodynamics; 5.4 Summary; References; Exercises |
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6 Generalized Hydrodynamics Beyond Navier-Stokes6.1 Grad's Thirteen-Moment Theory; 6.2 Grad's Approach in (Some) More Detail; 6.3 R13: Regularized Grad-13 Expansion; 6.4 Linearized Collision Operator; 6.4.1 The CSF Spectral Decomposition; 6.5 Summary: Grad versus Chapman-Enskog; References; Exercises; 7 Kinetic Theory of Dense Fluids; 7.1 Cautionary Remark; 7.2 Finite-Density Extension of the Boltzmann Equation; 7.3 The BBGKY Hierarchy; 7.3.1 Statistical Mechanics: The Liouville Equation; 7.3.2 Liouville Theorem; 7.3.3 Taking Averages; 7.3.4 Many-Body Equilibria of the Liouville Equation |
| Summary |
An introductory textbook to Lattice Boltzmann methods in computational fluid dynamics, aimed at a broad audience of scientists working with flowing matter. LB has known a burgeoning growth of applications, especially in connection with the simulation of complex flows, and also on the methodological side |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed April 12, 2018) |
| Subject |
Transport theory.
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Lattice theory.
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Evolution equations.
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SCIENCE -- Energy.
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Physics -- General.
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Evolution equations
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Lattice theory
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Transport theory
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| Form |
Electronic book
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| ISBN |
9780192538857 |
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0192538853 |
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9780191847967 |
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0191847968 |
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