With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.

Lattice-Boltzmann Method for Complex Flows

Preface 1. Introduction 2. Cellular automata modeling 3. Statistical mechanics of lattice gas 4. Diffusion phenomena 5. Reaction-diffusion processes 6. Non-equilibrium phase transitions 7. Other models and applications Bibliography Glossary Index.

Cellular automata modeling of physical systems

Viscous flow computations with the method of lattice Boltzmann equation

Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.

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Dieter A. Wolf-Gladrow

Papers

Lattice-Gas Cellular Automata and Lattice Boltzmann Models