The Lattice Boltzmann Equation ― For Complex States of Flowing Matter

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.

Sauro Succi, Director of Research, Istituto Applicazioni del Calcolo "Mauro Picone", Rome, National Research Council of Italy

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.