LAUM, CNRS, Université du Maine, Avenue Olivier Messiaen, 72085 Le Mans, France.
J Acoust Soc Am. 2011 Mar;129(3):1240-9. doi: 10.1121/1.3531928.
In modeling the wave propagation within a street canyon, particular attention must be paid to the description of both the multiple reflections of the wave on the building facades and the radiation in the free space above the street. The street canyon being considered as an open waveguide with a discontinuously varying cross-section, a coupled modal-finite element formulation is proposed to solve the three-dimensional wave equation within. The originally open configuration-the street canyon open in the sky above-is artificially turned into a close waveguiding structure by using perfectly matched layers that truncate the infinite sky without introducing numerical reflection. Then the eigenmodes of the resulting waveguide are determined by a finite element method computation in the cross-section. The eigensolutions can finally be used in a multimodal formulation of the wave propagation along the canyon, given its geometry and the end conditions at its extremities: initial field condition at the entrance and radiation condition at the output.
在对街道峡谷内的波传播进行建模时，必须特别注意描述波在建筑物立面上的多次反射和在街道上方自由空间中的辐射。由于街道峡谷被视为具有不连续变化的横截面的开放式波导，因此提出了一种耦合模态有限元公式来解决其中的三维波动方程。原本开放的配置——天空中开放的街道峡谷——通过使用完美匹配层被人为地变成了一个封闭的波导结构，这种方法截断了无限的天空，而不会引入数值反射。然后，通过在横截面上进行有限元方法计算来确定得到的波导的本征模。最后，可以根据峡谷的几何形状和其两端的边界条件（入口处的初始场条件和输出处的辐射条件），在峡谷中的波传播的多模态公式中使用这些本征解。
