Lattice Gas Models for Sound Propagation Simulation.

New lattice gas models for sound propagation are studied in this thesis. The one dimensional (1-D) model has zero truncation error, and the group velocity is independent of wave number as is required from the continuum limit. Conventional finite difference approaches do not have these properties in general. Boundary condition treatments, applicable to the 1-D model, are also given. Both the boundary between two fluid media and an impedance boundary are considered. An extension of the 1-D model to two dimensional (2-D) models is also discussed. A variation on standard splitting methods is used to extend the formulation developed for the 1-D model in order to obtain 2-D models. A model for a 2-D square lattice and a model for a 2-D hexagonal lattice are obtained. In arbitrary directions of propagation the methods are at least second order accurate. However, the accuracy of the 2-D square lattice model is greatly increased for narrow angle propagation along the coordinate axes. Dissipation effects can be included into these lattice gas wave models. To simulate dissipation effects, lattice gas particles are assumed to take a random walk. A method to improve the simulation of dissipation is also obtained. A different formulation of the above 1-D and 2 -D models is also developed. This formulation requires less computer memory in most cases than the original formulation. This formulation also provides a way to include fluid dynamic nonlinear effects into the lattice gas wave models. Using this formulation, lattice gas models for Burgers' equation and the 1-D Euler equations are obtained. This formulation is also used to obtain a lattice gas model for sound propagation in a moving medium.