## The Lattice Boltzmann Equation: For Fluid Dynamics and BeyondIn recent years, stylized forms of the Boltzmann equation, now going by the name of "Lattice Boltzmann equation" (LBE), have emerged, which relinquish most mathematical complexities of the true Boltzmann equation without sacrificing physical fidelity in the description of many situations involving complex fluid motion. This book provides the first detailed survey of LBE theory and its major applications to date. Accessible to a broad audience of scientists dealing with complex system dynamics, the book also portrays future developments in allied areas of science (material science, biology etc.) where fluid motion plays a distinguished role. |

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### Contents

Kinetic theory | 3 |

Lattice Gas Cellular Automata | 17 |

Lattice Boltzmann models with underlying Boolean | 40 |

Lattice Boltzmann models without underlying Boolean | 51 |

Lattice BhatnagarGrossKrook | 65 |

FLUID DYNAMICS APPLICATIONS AND ADVANCED | 75 |

Flows at moderate Reynolds number | 97 |

LBE flows in disordered media | 110 |

LBE in the framework of computational fluid | 155 |

BEYOND FLUID DYNAMICS | 177 |

LBE for quantum mechanics | 214 |

equation | 216 |

Thermohydrodynamic LBE schemes | 233 |

Who needs LBE? | 254 |

263 | |

281 | |

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### Common terms and phrases

applications basic Boltzmann equation Boolean boundary conditions cellular automata chapter coefficients collision operator collisional complex computational fluid dynamics conservation constraints continuum corresponding density derivatives diffusion dimensions Dirac equation discrete speeds dissipation distribution function effects eigenvalues energy equilibria explicit expression f f f FCHC finite difference finite volume flow speed fluctuations fluid dynamics Galilean invariance gradient grid hydrodynamic incompressible interactions interface invariance kinetic theory Lagrangian lattice Boltzmann lattice gas lattice units LBE schemes LBE simulations LBGK LGCA linear Mach number macroscopic mass mean free path microdynamics molecular molecular dynamics molecules momentum flux tensor multiphase Navier-Stokes equations numerical scheme parallel computing parameters particle physical Poiseuille flow populations porous media potential pressure problem quantum LBE quasilinear LBE result Reynolds number scales scattering matrix second-order simple solid space space-time spatial streaming operator symmetry temperature theorem thermal thermodynamic time-step turbulent flows typical velocity viscosity wall