The paper describes a combination of a preconditioning method with a high-order compact discretization scheme for the purpose of solving the compressible Navier–Stokes equations in moderate and low Mach number regimes. When combined with properly modified characteristic boundary conditions, the proposed approach is very efficient from the point of view of convergence acceleration and accuracy of the results. The computations were performed in typical benchmark cases including the Burggraf flow for which an analytical solution exists, the flow over a backward facing step, and also the flow in 2D and 3D shear-driven cavities. Depending on the test case, the results were obtained for the Mach number in the range M = 0.001 − 0.5 and the Reynolds number Re = 1 − 1000. Copyright © 2012 John Wiley & Sons, Ltd.