  In this paper, exact solutions to the problem of acoustic scattering by
elastic spherical symmetric scatterers are developed. The scatterer may consist
of an arbitrary number of fluid and solid layers, and scattering with single
Neumann conditions (replacing Neumann-to-Neumann conditions) is added. The
solution is obtained by separation of variables, resulting in an infinite
series which must be truncated for numerical evaluation. The implemented
numerical solution is exact in the sense that numerical error is solely due to
round-off errors, which will be shown using the symbolic toolbox in MATLAB. A
system of benchmark problems is proposed for future reference. Numerical
examples are presented, including comparisons with reference solutions,
far-field patterns and near-field plots of the benchmark problems, and
time-dependent solutions obtained by Fourier transformation.
