Transmission line matrix model: numerical dispersion effects on simulated specular reflection

Numerical sound propagation models include a wide range of methods with their own advantages depending on the physical phenomena under consideration. Due to its low-order scheme characteristic, the transmission line matrix (TLM) model is considered for coarse modeling of sound fields in complex outdoor environments. However, the space-time integration scheme of the method is dispersive and affects the free-field predictions. This paper extends a previous study of the numerical dispersion effect on the acoustic pressure field. An ideal case with specular reflections on a perfectly reflective ground is considered to represent the worst-case scenario, as the absence of absorption by the boundary maximizes the influence of numerical dispersion. First, a reminder of the model boundary conditions for specular reflection is provided, and the corresponding analytical solution is introduced as a reference to evaluate the reliability of the model. Then, a numerical experiment is presented and performed for different sound source characteristics. The result analysis shows that dispersion can induce misplaced interferences in the numerically simulated sound fields and the resulting errors are quantified in terms of sound pressure levels (SPL). Finally, an analytical comparison with a well-known finite difference numerical scheme gives a perspective on the TLM model performance regarding several applications.