A pressure-based procedure able to model all Mach number flows is presented. The scheme uses curvilinear coordinates and a composite low-high-order treatment with the normalized variable diagram as limiter for the convective terms. The Cartesian components of the velocity are used as dependent variables in the momentum equations and the extension of the SIMPLE method to include the compressibility effects is presented for a non-staggered grid arrangement. Comparison of the calculations with available numerical and experimental data shows that the method is accurate, self-adaptive and stable for a wide range of Mach numbers. The shock resolution is noticeably improved by using a high-order scheme for the convective term treatment.