Factors that influence the calculation of acoustic scattering by the method of source simulation

In this work the source simulation technique was used to
calculate the scattering of a plane wave by a cylinder with radial or elliptical
transverse section. The basic idea of the source simulation technique is to
replace the scattering (or radiating) body with a system of simple sources
located within the envelope of the scatterer (or radiator). The extent to which
the simulated field reproduces the original one depends on the degree of
correspondence between the simulated and the given boundary conditions.
Numerical simulations have shown that: 1) the shape of the auxiliary surface; 2)
the number of sources, and 3) the way the sources are distributed are the most
relevant parameters to ensure an accurate solution of the problem. In the case
of the single-layer method, the sources should not be positioned close to the
surface or to the center of the body, because the problem becomes
ill-conditioned. The auxiliary surface and the acatterer should be as similar as
possible in order to minimize the boundary error. With respect to the number of
sources (N), there are two opposite effects: 1) if (N) is too
small, the sound field is not reproduced accurately; 2) if (N) is too
large, the computing time increases and the solution accuracy decreases. The
method breaks down when the excitation frequency coincides with the
eigenfrequenciec - a narrow range of frequencies - of the space formed by the
auxiliary surface. As the auxiliary surface is frequently represented by simple
surfaces (cylinder, sphere), one can easily calculate the eigenfrequencies and
therefore avoid them.