The Lattice Boltzmann Equation

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.

Flowing matter is all around us, from daily-life vital processes (breathing, blood circulation), to industrial, environmental, biological, and medical sciences. Complex states of flowing matter are equally present in fundamental physical processes, far remote from our direct senses, such as quantum-relativistic matter under ultra-high temperature conditions (quark-gluon plasmas). Capturing the complexities of such states of matter stands as one of the most prominent challenges of modern science, with multiple ramifications to physics, biology, mathematics, and computer science. As a result, mathematical and computational techniques capable of providing a quantitative account of the way that such complex states of flowing matter behave in space and time are becoming increasingly important. This book provides a unique description of a major technique, the Lattice Boltzmann method to accomplish this task.

The Lattice Boltzmann method has gained a prominent role as an efficient computational tool for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales; from fully-developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic sub-nuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this text provides a survey of the major developments which have led to the impressive growth of the Lattice Boltzmann across most walks of fluid dynamics and its interfaces with allied disciplines.

Included are recent developments of Lattice Boltzmann methods for non-ideal fluids, micro- and nanofluidic flows with suspended bodies of assorted nature and extensions to strong non-equilibrium flows beyond the realm of continuum fluid mechanics. In the final part, it presents the extension of the Lattice Boltzmann method to quantum and relativistic matter, in an attempt to match the major surge of interest spurred by recent developments in the area of strongly interacting holographic fluids, such as electron flows in graphene.

"It is important to register that this book in underpinned by strong pedagogical principles. This is not an arcane monograph but rather a text to get to grips with this extremely disparate topicone is confident that this book will serve very well the community of researchers who ply their trade using the Lattice Boltzmann equation." -- K. Alan Shore, Contemporary Physics Journal

Autorentext

Dr Sauro Succi holds a degree in Nuclear Engineering from the University of Bologna and a PhD in Plasma Physics from the EPFL, Lausanne. Since 1995 he serves as a Director of Research at the Istituto Applicazioni Calcolo of the Italian National Research Council in Rome and also as Research Associate of the Physics Department of Harvard University and a Visiting Professor at the Institute of Applied Computational Science at the School of Engineering and Applied Sciences of Harvard University. He has published extensively on a broad range of topics in computational kinetic theory and non-equilibrium statistical physics, including thermonuclear plasmas, fluid turbulence, micro and nanofluidics, as well as quantum-relativistic flows.

Inhalt

• Part I: Kinetic Theory of Fluids

• 1: Why a kinetic theory of fluids?

• 2: Kinetic theory and the Boltzmann equation

• 3: Approach to equilibrium, the H-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 kinetic theory

• 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 mircodynamics

• 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 number

• 19: LBE flows in disordered media

• 20: Lattice Boltzmann for Turbulent Flows

• Part IV: Lattice Kinetic Theory: Advanced Topics

• 21: Entropic Lattice Boltzmann

• 22: Thermohydrodynamics 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: Reactive flows

• 27: Lattice Boltzmann for non-ideal fluids

• 28: Extensions of the psuedo-potential methods

• 29: Lattice Boltzmann models for microflows

• 30: The fluctuating Lattice Boltzmann

• 31: Lattice Boltzmann for flows with suspended objects: fluid-solid interactions

• Part VI: Beyond Newtonian Mechanics: Quantum and Relativistic Fluids

• 32: LBE for quantum mechanics

• 33: QLB for quantum many-body and quantum field theory

• 34: Relativistic Lattice Boltzmann

• 35: Relativistiv Lattice Boltzmann II: kinetic derivation

• 36: Coda

• 37: Notation

• Appendices