This paper combines a state-of-the-art method for solving the preconditioned compressible Navier-Stokes equations accurately and efficiently for a wide range of the Mach number with an immersed-boundary approach which allows to use Cartesian grids for arbitrarily complex geometries. The method is validated versus well documented test problems for a wide range of the Reynolds and Mach numbers. The numerical results demonstrate the efficiency and versatility of the proposed approach as well as its accuracy, from incompressible to supersonic flow conditions, for moderate values of the Reynolds number. Further improvements, obtained via local grid refinement or nonlinear wall functions, can render the proposed approach a formidable tool for studying complex three-dimensional flows of industrial interest.
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