- 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

# Numerical Methods for the Kinetic Theory of Fluids

# Numerical Methods for the Kinetic Theory of Fluids

- Chapter:
- (p.157) 10 Numerical Methods for the Kinetic Theory of Fluids
- Source:
- The Lattice Boltzmann Equation
- Author(s):
### Sauro Succi

- Publisher:
- Oxford University Press

This chapter provides a bird’s eye view of the main numerical particle methods used in the kinetic theory of fluids, the main purpose being of locating Lattice Boltzmann in the broader context of computational kinetic theory. The leading numerical methods for dense and rarified fluids are Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC), respectively. These methods date of the mid 50s and 60s, respectively, and, ever since, they have undergone a series of impressive developments and refinements which have turned them in major tools of investigation, discovery and design. However, they are both very demanding on computational grounds, which motivates a ceaseless demand for new and improved variants aimed at enhancing their computational efficiency without losing physical fidelity and vice versa, enhance their physical fidelity without compromising computational viability.

*Keywords:*
Kinetic theory of fluids, numerical methods, computational kinetic theory, Direct Simulation Monte Carlo, mesoparticle methods

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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