  The acoustic equations derived as a linearization of the Euler equations are
a valuable system for studies of multi-dimensional solutions. Additionally they
possess a low Mach number limit analogous to that of the Euler equations.
Aiming at understanding the behaviour of the multi-dimensional Godunov scheme
in this limit, first the exact solution of the corresponding Cauchy problem in
three spatial dimensions is derived. The appearance of logarithmic
singularities in the exact solution of the 4-quadrant Riemann Problem in two
dimensions is discussed. The solution formulae are then used to obtain the
multidimensional Godunov finite volume scheme in two dimensions. It is shown to
be superior to the dimensionally split upwind/Roe scheme concerning its domain
of stability and ability to resolve multi-dimensional Riemann problems. It is
shown experimentally and theoretically that despite taking into account
multi-dimensional information it is, however, not able to resolve the low Mach
number limit.
