Lattice Boltzmann method and its applications

The lattice Boltzmann method (LBM) is a numerical mesoscopic approach originated from the lattice gas automata method. In LBM, the concept of distribution function that implies the possibility of finding particles with a specified velocity range in a specified location and time is used to recover governing equations of transport phenomenon. Compared to the traditional computational fluid dynamics method LBM has some advantages including, easy handling of complex geometries and boundary conditions, and parallel simulations. Besides, the pressure field can easily be obtained once the density field is solved using the distribution function concept, so there is no need to solve the computationally expensive Poisson equation. The chapter aims to provide an overview of the theory, practice, and implementation of the LBM and to provide students, researchers, and engineers with sample codes so that they can immediately apply their knowledge to practical applications. In this chapter, first, single relaxation time and multirelaxation time LBM and their boundaries were presented. Then classifying the various models, thermal LBM, multicomponent and multiphase LBM were described in terms of the derived macroscopic equations. Finally, some application examples were provided.