A Numerical Method for Predicting Acoustical Wave Propagation in Open Spaces

Abstract

We present a numerical methodology for evaluating wave propagation phenomena in two dimensions in the time domain with focus on the linear acoustic second-order wave equation. An outline of the higher-order compact discretization schemes followed by the time discretization technique is first presented. The method is completed with the addition of spatial filtering based on the same compact schemes' principles. The important role of boundary conditions is subsequently addressed. Two popular ways to truncate the computational domain in the near field are presented and compared here: first the formulation of “absorbing conditions” in the form of partial differential equations especially for the origin and second the construction of an absorbing layer surrounding the domain, in which waves (after they have exited the domain) are attenuated and decayed exponentially. Subsequently, the method is assessed by recalling three benchmark problems. In the first where a Gaussian pulse is generated and propagated in a 2D rectangular domain, the accuracy and absorbability of the boundary conditions are compared. In the second, a similar situation is investigated but under curvilinear coordinates and under the presence of a solid body which scatters the pulse. Finally the sound field inducted by the flow of corotating vortex pair is calculated and compared with the corresponding analytical solution.