Foreword

Lattice Boltzmann Methods (LBM) emerged over twenty years ago as a new way of analyzing physical systems, mostly of the fluid flow type. While historically LBM evolved from lattice gas automata models, it is now better interpreted as a systematic approximation to the Boltzmann kinetic theory. Unlike a real microscopic many-body system, LBM represents a fluid system as a simple dynamical model residing in some special discrete phase space. The governing equation resulting from such formulation is called lattice Boltzmann equation. Although an LBM model is a drastic simplification to the corresponding realistic fluid system at the micro-dynamical level, correct physical properties at the macroscopic level can be shown to be recovered with proper formulation. This fact allows using LBM as an alternative computational fluid dynamics (CFD) approach for studying realistic physical phenomena. The fundamental difference between LBM and conventional CFD is that the former is based on a microscopic (or perhaps “mesoscopic”) level description via Boltzmann - like kinetic equation, instead of solving hydrodynamic equations such as the Navier-Stokes equation. This difference has enabled a number of key advantages of LBM over the conventional approach. In addition to the familiar benefits such as being an attractive computational method for efficient and robust fluid simulation, LBM, due to its underlying kinetic theory basis also opens a way to simulate a wider variety of hydrodynamic phenomena for a broader range of physical regimes than the conventional computational methods. Many of such problems known to be extremely difficult or impossible to treat by the conventional techniques can be now approached.

Besides the basic scientific interest associated with LBM, this new field has a significant potential in real world applications. With the rapid progress in the information and computer technologies, computer aided engineering (CAE) has now become the leading trend in modern industrial engineering processes. The computer - based process allows a virtual platform for studying physical problems often impossible in real experiment, thus enabling deeper understanding of the underlying phenomena. Consequently, the new process greatly enhances and empowers innovation. In this context, LBM is not only offering great opportunities in the fluid dynamics area but is already making substantial impact in the CAE - based real world engineering process.

In the recent years LBM has become a very active and fast growing research field, as evident from the richness of topics covered in this eBook. This method now is not only standing on a much more solid theoretical foundation but also has a substantially expanded domain of applications. Comparing to the early years when LBM only described the simple Navier-Stokes fluids, it is now used to handle a wide variety of complex fluids and flows, as well as physical systems beyond fluid dynamics. As indicated in the title, this eBook covers a set of important extensions in LBM ranging from reacting flows to transport phenomena to fluid-solid interactions. Such problems are of central importance in many real world applications. LBM models of these physical systems open a way for deeper understanding of their essential physical properties. In addition to these extensions, the eBook also includes some of the state of the art theoretical underpinnings in LBM fundamentals and formulations. This eBook edited by Professor Matthias Ehrhardt will certainly be useful for a large audience of scholars.