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. |
Contents
THEORY | 1 |
2 | 9 |
1 | 15 |
4 | 30 |
6 | 38 |
Lattice Boltzmann models without underlying Boolean | 51 |
Lattice BhatnagarGrossKrook | 64 |
FLUID DYNAMICS APPLICATIONS AND ADVANCED | 75 |
LBE flows in disordered media | 110 |
Turbulent flows | 124 |
geoflexible lattice Boltzmann | 142 |
LBE in the framework of computational fluid | 155 |
BEYOND FLUID DYNAMICS | 177 |
LBE for quantum mechanics | 214 |
Thermohydrodynamic LBE schemes | 233 |
Who needs LBE? | 254 |
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Common terms and phrases
applications basic Bhatnagar-Gross-Krook Boltzmann equation Boolean bounce-back boundary conditions cellular automata chapter Chen coefficient collision operator collisional complex conservation constraints corresponding density derivatives diffusion Digital Physics dimensions Dirac equation discrete speeds distribution function effects eigenvalue energy equilibria explicit expression FCHC finite difference finite volume flow speed fluctuations fluid dynamics fluid flow Galilean invariance gradient grid H-theorem hydrodynamic incompressible interaction interface kinetic theory Lagrangian lattice gas lattice units LBE schemes LBE simulations LBGK LGCA linear Mach number macroscopic mass mean free path methods molecular molecules momentum flux tensor multiphase Navier-Stokes equations nonlinear parallel computing parameters particle Phys physical Poiseuille flow populations porous media potential pressure problem pseudospectral quantum LBE quasilinear LBE relaxation result Reynolds number scales scattering matrix Schrödinger equation second-order simple solid space space-time spatial stability surface temperature thermal thermodynamic time-step turbulent flows typical values velocity viscosity wall