The Lattice Boltzmann Method

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the methods background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special in a nutshell sections that condense the chapters most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.

Part I Background: Basics of hydrodynamics and kinetic theory.- Numerical methods for fluids.- Part II Lattice Boltzmann fundamentals: The lattice Boltzmann equation.- Analysis of the lattice Boltzmann equation.- Boundary and initial conditions.- Forces.- Non-dimensionalisation and choice of simulation parameters.- Part III Lattice Boltzmann extensions, improvements, and details: Lattice-Boltzmann for advection-diffusion-problems.- Multiphase and multi-component flows.- MRT and TRT collision operators.- Boundary conditions for fluid-structure interaction.- Sound waves.- Part IV Numerical implementation of the lattice Boltzmann method: Implementation of LB Simulations.- Appendices.