One‐dimensional transport equation models for sound energy propagation in long spaces.

Abstract

In this paper, a three‐dimensional transport equation model is first presented to describe the sound energy propagation in a long space. Then the three‐dimensional model is reduced to a one‐dimensional model by approximating the solution using the method of weighted residuals. The one‐dimensional transport equation model directly describes the sound energy propagation in the long dimension and deals with the sound energy across the cross‐section by prescribed functions. The one‐dimensional transport equation model consists of a coupled set of N transport equations. Only N = 1 and N = 2 are discussed in this paper. For larger N, although the accuracy could be improved, the calculation time is expected to be significantly longer, which diminishes the advantage of the one‐dimensional model over the three‐dimensional model in terms of the computational efficiency. Some simulation results are provided in comparison with the ray‐tracing based approach, which show good agreement.