Finite Difference Analysis of 2-Dimensional Acoustic Wave with a Signal Function

Abstract

This paper describes progress on a two dimensional numerical simulation of acoustic wave propagation that has been developed to visualize the propagation of acoustic wave fronts and to provide time-domain signal. In this exercise, we have simulated propagation of sound in such a medium using both explicit and Crank Nicolson finite difference schemes, we have also tested for stability of the developed schemes using Vonn Newmann and Matrix stability analysis together with its associated code in matlab. The stability analyses of the developed schemes revealed that Explicit scheme was conditionally stable while the Hybrid one (Crank Nicolson Scheme) was unconditionally stable, for all values of courant number r. The rate of convergence of the algorithms depend on the truncation error introduced when approximating the partial derivatives, the Crank-Nicolson method converged at the rate of (k2+ h2), which is a faster rate of convergence than either the explicit method, or the implicit method.