Analysis of the numerical properties of the transmission line matrix model for outdoor sound propagation

Outdoor sound propagation modeling can be performed through various numerical models. Nowadays, time-domain methods are widely used and enable accurate simulations for most of the sound physical phenomena involved in environmental acoustics. However, the transmission line matrix (TLM) method remains relatively poorly documented. In this paper, a thorough review of the method and a stability analysis are provided. The review of the model leads to a more robust understanding of its link with the wave equation using Taylor expansions. Two different cases are considered: a homogeneous non-dissipative medium and an inhomogeneous dissipative one. The stability analysis shows the quantification of the model inherent dispersion error and highlights similarities with a finite difference scheme. To conclude, a numerical experiment aims to characterize precisely the limitations of the method applied to outdoor sound propagation.