Granular Gas Dynamics

Thorsten Pöschel, Nikolai V. Brilliantov

Springer Science & Business Media, Oct 16, 2003 - Science - 369 pages

The contributions in this book address both the kinetic approach one using the Boltzmann equation for dissipative gases as well as the less established hydrodynamic description. The last part of the book is devoted to driven granular gases and their analogy with molecular fluids.

Contents

• Asymptotic Solutions of the Nonlinear Boltzmann Equation for Dissipative Systems: 1
• 2 Inelastic BGK Model: 4
• 3 Basics of Inelastic Scattering Models: 7
• 4 Analysis of Inelastic Scattering Models: 16
• 5 Inelastic Maxwell Models: 23
• 6 Conclusions and Perspectives: 29
• References: 32
• The Homogeneous Cooling State Revisited: 35
• 2 Setting Up the Problem: 37
• 3 Heuristic Analysis: 38
• 4 The NearMaxwellian Range of Speeds: 43
• 5 Reduction of the Boltzmann Equation for the HCS: 45
• 6 Concluding Remarks: 51
• References: 59
• The Inelastic Maxwell Model: 63
• One Dimension: 65
• Arbitrary Dimension: 71
• 4 Impurities: 78
• 5 Mixtures: 84
• 6 Lattice Gases: 86
• 7 Conclusions: 88
• References: 90
• Velocity Fluctuations in Cooling Granular Gases: 93
• 2 Instabilities of the Homogeneous Cooling State: 94
• The Homogeneous Inelastic Maxwell Model: 98
• 4 The OneDimensional Gas: 101
• 5 The TwoDimensional Gas: 105
• 6 Conclusions: 113
• References: 114
• SelfSimilar Asymptotics for the Boltzmann Equation with Inelastic Interactions: 117
• 2 Isotropic Equation and Preliminary Result: 119
• Preliminaries: 121
• 4 Complete Proof of the Conjecture: 125
• References: 127
• Kinetic Integrals in the Kinetic Theory of Dissipative Gases: 129
• 2 A Simple Example: 131
• 3 Granular Gases of Viscoelastic Particles: 134
• 4 Evaluation of Kinetic Integrals: 135
• 5 Computational Formula Manipulation to Evaluate Kinetic Integrals: 143
• 6 Kinetic Integrals in the Kinetic Theory of Granular Gases: 150
• 7 Conclusion: 159
• Kinetics of Fragmenting Freely Evolving Granular Gases: 161
• 2 Model: 162
• 3 Kinetics: 164
• 4 Numerical Simulations: 170
• 5 Discussion: 179
• References: 181
• Granular Hydrodynamics: 183
• Shock Waves in Granular Gases: 185
• 2 OneDimensional Waves: 188
• 3 TwoDimensional Waves: 200
• 4 Waves in Vibrated Granular Media: 205
• 5 Summary: 218
• References: 220
• Linearized Boltzmann Equation and Hydrodynamics for Granular Gases: 225
• 2 Nonlinear Boltzmann Equation and the Homogeneous Cooling State: 227
• 3 Linearized Boltzmann Equation: 231
• 4 Eigenvalue Problem: 234
• 5 NavierStokes and GreenKubo Expressions: 239
• 6 Discussion: 244
• References: 246
• Development of a Density Inversion in Driven Granular Gases: 249
• 2 The Model Problem and Hydrodynamic Equations: 251
• 3 Steady State Profiles and Density Inversion: 255
• LowMachNumber Flow: 257
• Early Times: 260
• 6 Discussion: 262
• References: 263
• Kinetic Theory for Inertia Flows of Dilute Turbulent GasSolids Mixtures: 265
• 2 GasSolids Interactions: 267
• 3 Granular Transport Theory: 269
• 4 Moment Method: 273
• 5 Mixture Theory: 274
• 6 Turbulence Modulation: 274
• 7 Application: 276
• 8 Comparisons between Predictions and Experiments: 277
• 9 Conclusion: 279
• References: 280
• Driven Gases and Structure Formation: 285
• Driven Granular Gases: 287
• 2 The Model: 289
• 4 Numerical Simulations: 295
• 5 Simulations with Rotation: 299
• 6 Analytical Study of the Velocity Distribution: 301
• 7 Summary and Conclusions: 305
• References: 308
• Van der WaalsLike Transition in Fluidized Granular Matter: 311
• References: 326
• Birth and Sudden Death of a Granular Cluster: 329
• 2 Flux Model: 331
• Hysteresis: 332
• 4 Coarsening and Sudden Death: 333
• Antidiffusion: 337
• 6 Extensions and Applications: 339
• References: 340
• Vibrated Granular Media as Experimentally Realizable Granular Gases: 341
• 2 Description of the Simulations: 342
• 3 Comparison of Simulation and Experiment: 344
• 4 Effects of Clustering n 2 or 3: 350
• 5 Conclusions: 358
• References: 359

Popular passages

Page xi - H. Eugene Stanley Center for Polymer Studies and Department of Physics Boston University, Boston, MA 02215 USA...‎

Page x - Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978.‎

Page x - School of Physics and Astronomy, Tel Aviv University Tel Aviv 69978, Israel...‎

Page xii - CA (Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 5487, Santiago, Chile).‎

Bibliographic information

• Title: Granular Gas Dynamics; Volume 624 of Lecture Notes in Physics
• Editors: Thorsten Pöschel, Nikolai V. Brilliantov
• Edition: illustrated
• Publisher: Springer Science & Business Media, 2003
• ISBN: 3540201106, 9783540201106
• Length: 369 pages
• Subjects: Science / Mechanics / Fluids; Science / Mechanics / General; Science / Mechanics / Solids; Science / Physics / Condensed Matter; Science / Physics / General; Technology & Engineering / Mechanical