A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suited to simulate
flows at all levels of Mach number with smooth and discontinuous flow field changes, by providing
a precise representation of convective transport and acoustic propagation. The co-located finite volume
space discretisation is used with the AUSM flux splitting. It is demonstrated that two ingredients are
essential for obtaining good quality solutions : the presence of an inertia term in the transporting velocity
expression ; a velocity difference diffusive term in the face pressure expression, with a correct Mach
number scaling to recover the hydrodynamic and acoustic low Mach number limits. To meet these two
requirements, a new flux scheme, named MIAU, for Momentum Interpolation with Advection Upstream
splitting is proposed
