In modeling the wave propagation within an urban, U-shaped, street canyon, a particular attention must be paid to the description of the radiation of the wave in the free space above the street, and to its multiple reflections on the building facades, due to their irregularity. The street canyon being considered as an open waveguide in which the sound, generated by some source, may propagate, the authors have shown how a multimodal approach of the wave propagation can be formulated, that takes into account the opening of the street on the free space above. Moreover, such a formalism is particularly adapted to take into account geometrical or physical non-uniformities in the waveguide, as well as the radiation or continuity conditions at the extremities. The key point when establishing the multimodal method is the computation of the local transverse problem, in the cross-section of the street; then the propagation along the waveguide can be solved analytically. The aim of the present work is mainly to show how the original problem of an open waveguide can be substituted for new problem of a closed, heterogeneous, waveguide by using Perfectly Matched Layers (PML). This reformulation enables an efficient and accurate coupled FEM - modal solution of the problem, that is detailed and discussed. It is notably shown how to take into account the variations of the cross-section, due to the facade irregularities.
展开▼
