  The problem of scattering of harmonic plane acoustic waves by fluid spheroids
(prolate and oblate) is addressed from an analytical approach. Mathematically,
it consists in solving the Helmholtz equation in an unbounded domain with
Sommerfeld radiation condition at infinity. The domain where propagation takes
place is characterised by density and sound speed values $\rho_0$ and $c_0$,
respectively, while $\rho_1$ and $c_1$ are the corresponding density and sound
speed values of an immersed object that is responsible of the scattered field.
Since Helmholtz equation is separable in prolate/oblate spheroidal coordinates,
its exact solution for the scattered field can be expressed as an expansion on
prolate/oblate spheroidal functions multiplied by coefficients whose values
depend upon the boundary conditions verified at the medium-immersed fluid
obstacle interface. The general case ($c_0 \neq c_1$) is cumbersome because it
requires to solve successive matrix systems that are ill-conditioned when
$c_1/c_0$ is far from unity. In this paper, a numerical implementation of the
general exact solution that is valid for any range of eccentricity values and
for $c_0 \neq c_1$, is provided. The high level solver code has been written in
the Julia programming language while a software package recently released in
the literature has been used to compute the spheroidal functions. Several limit
cases (Dirichlet and Neumann boundary conditions, spheroid tending to sphere)
have been satisfactorily verified using the implemented code. The corresponding
example scripts can be downloaded from the authors' web (GitHub) site.
Additionally, the new code has been used to extend results reported in the
literature.
