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

#### 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.

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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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**