Finite difference modeling of acoustic devices

The prevalent numerical approaches for modeling acoustic devices are the finite element method and methods based on transmission line analogs. In this work we explore the use of the finite difference method to solve the hyperbolic acoustic wave equation. The hyperbolic wave equation is usually difficult to solve numerically because it is second order in time and space, which predicates the use of a very small time step to keep the solution stable. There are implicit methods that are inherently stable when used to solve the difference equations, but they are difficult to implement. Here we report our implementation of an explicit method to solve the finite-difference scheme for acoustic wave problems. The first problem to be solved is that of a one-dimensional thickness mode bulk acoustic wave resonator excited by an electric field in the thickness direction (TE-mode resonator). Results are shown for a 2 MHz device at different frequencies. The graphs show the wave propagation as a function of time and space. The formulation of the problem with respect to the choice of both time and spatial steps is discussed.