### Application Of The Method Of Fundamental Solutions As A Coupling Procedure To Solve Outdoor Sound Propagation Problems

Sebastian Hampel, Adrían P. Cisilino, Sabine Langer

#### Abstract

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 nearfield
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 emission 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 a two-dimensional problem consisting of
a of a noise barrier in a homogeneous atmosphere, for which a reference solution is known.

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