An immersed-boundary method for compressible viscous flows

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 one to use Cartesian grids for arbi- trarily 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 incom- pressible to supersonic flow conditions, for moderate values of the Reynolds number. Further improvements, obtained via local grid refinement or non-linear wall functions, can render the proposed approach a formidable tool for studying complex three-dimensional flows of industrial interest.