- Title Pages
- Dedication
- Preface
- Acknowledgements
- Part I Kinetic Theory of Fluids
- 1 Why a Kinetic Theory of Fluids?
- 2 Boltzmann’s Kinetic Theory
- 3 Approach to Equilibrium, the <i>H</i>-Theorem and Irreversibility
- 4 Transport Phenomena
- 5 From Kinetic Theory to Navier–Stokes Hydrodynamics
- 6 Generalized Hydrodynamics Beyond Navier–Stokes
- 7 Kinetic Theory of Dense Fluids
- 8 Model Boltzmann Equations
- 9 Stochastic Particle Dynamics
- 10 Numerical Methods for the Kinetic Theory of Fluids
- Part II Lattice Kinetic Theory
- 11 Lattice Gas-Cellular Automata
- 12 Lattice Boltzmann Models with Underlying Boolean Microdynamics
- 13 Lattice Boltzmann Models without Underlying Boolean Microdynamics
- 14 Lattice Relaxation Schemes
- 15 The Hermite–Gauss Route to LBE
- 16 LBE in the Framework of Computational-Fluid Dynamics
- Part III Fluid Dynamics Applications
- 17 Boundary Conditions
- 18 Flows at Moderate Reynolds Numbers
- 19 LBE Flows in Disordered Media
- 20 Lattice Boltzmann for Turbulent Flows
- Part IV Lattice Kinetic Theory: Advanced Topics
- 21 Entropic Lattice Boltzmann
- 22 Thermohydrodynamic LBE Schemes
- 23 Out of Legoland: Geoflexible Lattice Boltzmann Equations
- 24 Lattice Boltzmann for Turbulence Modeling
- Part V Beyond Fluid Dynamics: Complex States of Flowing Matter
- 25 LBE for Generalized Hydrodynamics
- 26 Lattice Boltzmann for reactive flows
- 27 Lattice Boltzmann for Non-Ideal Fluids
- 28 Extensions of the Pseudo-Potential Method
- 29 Lattice Boltzmann Models for Microflows
- 30 The Fluctuating Lattice Boltzmann
- 31 LB for Flows with Suspended Objects: Fluid–Solid Interactions
- Part VI Beyond Newtonian Mechanics: Quantum and Relativistic Fluids
- 32 Quantum Lattice Boltzmann (QLB)
- 33 QLB for Quantum Many-Body and Quantum Field Theory
- 34 Relativistic Lattice Boltzmann (RLB)
- 35 Advanced RLB models
- 36 Coda
- 37 Notation
- Appendices
- Part VII Hands-On
- Index

# Why a Kinetic Theory of Fluids?

# Why a Kinetic Theory of Fluids?

- Chapter:
- (p.3) 1 Why a Kinetic Theory of Fluids?
- Source:
- The Lattice Boltzmann Equation
- Author(s):
### Sauro Succi

- Publisher:
- Oxford University Press

Fluid flows are a pervasive presence across most branches of human activity, including daily life. Although the basic equations governing the motion of fluid flows are known for two centuries (1822), since the work of Claude–Louis Navier (1785–1836) and Gabriel Stokes (1819–1903), these equations still set a formidable challenge to the quantitative, and sometimes even qualitative, understanding of the way fluid matter flows in space and time. Meteorological phenomena are among the most popular examples in point, but the challenge extends to many otherinstances of collective fluid motion, both in classical and quantum physics. This Chapter presents the Navier–Stokes equations of fluid mechanics and discuss the main motivations behind the kinetic approach to computational fluid dynamics.

*Keywords:*
Navier–Stokes equations, fluid flows, kinetic theory of fluids, collective motion, meteorological phenomena

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- Title Pages
- Dedication
- Preface
- Acknowledgements
- Part I Kinetic Theory of Fluids
- 1 Why a Kinetic Theory of Fluids?
- 2 Boltzmann’s Kinetic Theory
- 3 Approach to Equilibrium, the <i>H</i>-Theorem and Irreversibility
- 4 Transport Phenomena
- 5 From Kinetic Theory to Navier–Stokes Hydrodynamics
- 6 Generalized Hydrodynamics Beyond Navier–Stokes
- 7 Kinetic Theory of Dense Fluids
- 8 Model Boltzmann Equations
- 9 Stochastic Particle Dynamics
- 10 Numerical Methods for the Kinetic Theory of Fluids
- Part II Lattice Kinetic Theory
- 11 Lattice Gas-Cellular Automata
- 12 Lattice Boltzmann Models with Underlying Boolean Microdynamics
- 13 Lattice Boltzmann Models without Underlying Boolean Microdynamics
- 14 Lattice Relaxation Schemes
- 15 The Hermite–Gauss Route to LBE
- 16 LBE in the Framework of Computational-Fluid Dynamics
- Part III Fluid Dynamics Applications
- 17 Boundary Conditions
- 18 Flows at Moderate Reynolds Numbers
- 19 LBE Flows in Disordered Media
- 20 Lattice Boltzmann for Turbulent Flows
- Part IV Lattice Kinetic Theory: Advanced Topics
- 21 Entropic Lattice Boltzmann
- 22 Thermohydrodynamic LBE Schemes
- 23 Out of Legoland: Geoflexible Lattice Boltzmann Equations
- 24 Lattice Boltzmann for Turbulence Modeling
- Part V Beyond Fluid Dynamics: Complex States of Flowing Matter
- 25 LBE for Generalized Hydrodynamics
- 26 Lattice Boltzmann for reactive flows
- 27 Lattice Boltzmann for Non-Ideal Fluids
- 28 Extensions of the Pseudo-Potential Method
- 29 Lattice Boltzmann Models for Microflows
- 30 The Fluctuating Lattice Boltzmann
- 31 LB for Flows with Suspended Objects: Fluid–Solid Interactions
- Part VI Beyond Newtonian Mechanics: Quantum and Relativistic Fluids
- 32 Quantum Lattice Boltzmann (QLB)
- 33 QLB for Quantum Many-Body and Quantum Field Theory
- 34 Relativistic Lattice Boltzmann (RLB)
- 35 Advanced RLB models
- 36 Coda
- 37 Notation
- Appendices
- Part VII Hands-On
- Index