A simple absorbing layer implementation for transmission line matrix modeling
Résumé
An absorbing layer formulation for transmission line matrix modeling is proposed. The approach consists in attenuating the incident pulse propagating toward the absorbing layer only, using an attenuation factor which gradually decreases as the sound wave propagates along the absorbing medium. The formulation of the damping function followed by the attenuation factor along the absorbing layer is depicted and discussed. The efficiency of the present formulation is validated by comparison with another absorbing layer model and virtual boundary conditions proposed in the literature. Numerical simulations are also given in order to evaluate the effects of both the attenuation factor and the depth on the absorbing layer efficiency. As expected, results are consistent with absorbing layer implementation in other numerical methods; firstly, the attenuation at the entrance of the absorbing layer must be gentle, and secondly the efficiency increases with the layer depth. Lastly, it is shown that the unwanted reflection seems to vanish over the time when increasing the layer depth, meaning that reflections continuously occur within the absorbing layer and not on the geometrical limits of the absorbing layer. Although the approach is dedicated to outdoor sound propagation modeling (only an example on urban acoustics application is given), the proposed formulation of absorbing layers can be applied in other domains of acoustics. However, its application in shielded areas should be avoided because unwanted reflections due to an insufficient attenuation can be significant in comparison with the ambient noise in such quiet environments.