Application of the Method of the Fundamental Solutions to Couple the BEM and the Ray Method for Solving Outdoor Sound Propagation Problems

S. HAMPEL; A.P. CISILINO; S. LANGER

París, Francia

Conferencia; International Conference on Boundary Element Techniques BETEQ 2006; 2006

École Nationale des Ponts et Chaussées e Imperial College

In a computational model for outdoor sound propagation, the relevant propagation phenomena, among which are refraction and diffraction, must be implemented. All numerical methods applied in this field so far have disadvantages or limits. The Finite Element Method has to discretize the domain and hence is restricted to closed or at least moderate sized domains. The Boundary Element Method can hardly consider inhomogeneous domains and the computation effort increases exponentially for large systems. Geometric acoustics algorithms like ray tracing consider sound as particles and are hence not able to represent wave phenomena. It is the aim of this work to combine the advantages of the BEM and of the ray method: In the near-field where obstacles and complex geometries occur - and so diffraction and multiple reflection are expected - the model uses the BEM. Then, a ray model is coupled to compute the sound immission at large distances, because this model can take into account refraction resulting from wind or temperature profiles. The ray model requires point sources as input data. However, a boundary element calculation always delivers the pressure or its normal derivative along the boundary. Hence, for the coupling of both models it is necessary to convert the BEM results into equivalent point sources. The Method of Fundamental Solutions (MFS) is found suitable for this purpose. To couple the BEM and ray model, the acoustic half-space is divided into a BEM domain and a ray domain by defining a virtual interface. Along this interface, the pressure is computed with the BEM. The idea behind the MFS is to place a number of sources with unknown intensities around the domain of interest. These intensities are then computed in order to fulfill prescribed boundary conditions at discrete points on the boundary of the domain. The MFS can be either applied with fixed source positions or with an optimization algorithm, which finds the optimal source positions by minimizing the residual along the boundary in a least-squares sense. Both types of the MFS are used in this work. The verification of this new coupling procedure is shown for the case of a noise barrier in a homogeneous atmosphere, for which the exact solution is known.