A coupled modal-FE method for the sound propagation modeling in urban canyons

In modeling the sound propagation within an urban street canyon, a particular attention must be paid to the description of the radiation of the wave in the the free space above the street, as to its simple reflections on the buildings facades, due to their irregularity. The street canyon being considered as an open waveguide with a varying cross-section, a coupled modal-FE method was proposed in previous works [1, 2] to solve the three- dimensional wave equation within. The originally open configuration is first turned into a closed guiding structure by using perfectly matching layers (PML). Then, eigenmodes of the resulting waveguide are determined by a FEM computation on the transverse problem, and used in a multimodal formulation of the wave propagation within the canyon, given its geometry and the conditions at its extremities. This work presents the principles of this method as well as two relevant advances recently obtained. The first one deals with an alternative formulation of the problem, including a source term to obtain the modal-FE Green's function. The second one involves the extension of the method to the study of right-angled street intersections by adding an additional PML to the transverse cross-section, substituting the opening caused by the adjacent streets.