Lattice gas and lattice Boltzmann methods for simulation of hydrodynamics and magnetohydrodynamics

Lattice Gas Automata (LGA) methods and their extension, Lattice Boltzmann (LB) methods, have emerged in recent years as tools for modeling fluid dynamics and other systems described by partial differential equations. These schemes do not attempt to directly solve the equations, but rather to create a dynamics of fictitious particles in a lattice, whose macroscopic behavior corresponds to the Navier-Stokes equations, magneto-hydrodynamics (MHD) equations, or the equations of interest. In this thesis, the general principles are explained for the LGA methods first in the context of incompressible hydrodynamics, and then attempts to model MHD are described. Numerical simulations in the context of MHD are included. Likewise, we discuss the LB approach and describe the sequence of improvements that led to today's efficient models. Effective MHD LB models are also accounted for, along with the calculation of their transport properties. Comparisons of numerical experiments using LB methods and spectral methods that show the accuracy of the LB methods are included.