Copyright c  2007 ICCES ICCES, vol.3, no.3, pp.151-156, 2007 An immersed boundary technique using semi-structured grids for computing compressible viscous flows M.D. de Tullio 1 , P. De Palma 1 , G. Pascazio 1 and M. Napolitano 1 Summary This paper provides a numerical method based on the immersed boundary ap- proach for computing compressible viscous flows. The efficency of the method is enhanced by using a flexible local grid refinement technique which is obtained by coarsening a uniformly fine mesh far from high-gradient flow regions, such as boundary layers and shocks. Introduction The Immersed Boundary (IB) method simplifies the grid generation process for the simulation of flows with complex and/or moving solid boundaries by avoiding the need for a body-fitted mesh. The IB technique was originally developed for incompressible flows [1]-[3] using Cartesian grids. Recently, some of the authors have extended the IB technique to compressible flows [4] using the preconditioned Navier–Stokes equations, which allow one to provide accurate and efficient solu- tions for a wide range of the Mach number. To date, IB methods employ structured grids, which allow only limited control on the distribution of the grid points in the computational domain; in fact, clustering of grid points is needed close to solid boundaries in order to describe its geometry accurately and, since mesh lines run through the entire computational domain, a high concentration of grid points is ob- tained also in regions away from the solid walls, where flow gradients are usually small. In order to cope with this problem, a flexible local grid refinement technique is to be employed, increasing the mesh resolution near the body. Governing equations and numerical method In this work, the Reynolds Averaged Navier–Stokes (RANS) equations, written in terms of Favre mass-averaged quantities, are solved in conjunction with the low- Reynolds number k - ω turbulence model [5]. Such equations are given in compact form as: Γ ∂ Q v ∂τ + ∂ Q ∂ t + ∂ E ∂ x + ∂ F ∂ y + ∂ G ∂ z - ∂ E v ∂ x - ∂ F v ∂ y - ∂ G v ∂ z = D, (1) where Q is the conservative variable vector, E , F , G and E v , F v , G v indicate the inviscid and viscous fluxes, respectively, and D is the vector of the source terms. A pseudo-time derivative for the primitive variable vector Q v , which is related to Q by a Jacobian matrix, has been added to the left-hand-side of equation (1) in or- der to use a time marching approach for both steady and unsteady problems. The 1 DIMeG & CEMeC, Politecnico di Bari, via Re David 200, 70125, Bari, Italy