Exact solution and the multidimensional Godunov scheme for the acoustic equations

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