Summary: In the present paper we propose an extension of the direct-forcing immersed boundary technique, recently developed and employed by [R. Verzicco et al., J. Comput. Phys. 161, No. 1, 35–60 (2000; Zbl 0972.76073)], and successively improved by [{it E.A. Balaras} et al., J. Comput. Phys. 191, No. 2, 660–669 (2003; Zbl 1134.76406)]. We extend the aforementioned technique to curvilinear-coordinate, structured grid, Navier-Stokes solvers. This improved technique allows for more flexibility and efficiency when compared to standard methods in which the technique is coupled with orthogonal-grid solvers. Additional modifications are also proposed with respect to the state-of-art, which allow to deal with general shaped, multiple-body immersed surfaces and to make the interpolation of the velocity field off the body suitable for curvilinear grids. Several tests have been carried out to check the reliability of the proposed technique: first we have considered the three-dimensional Stokes flow around a sphere, and compared the numerical results with the analytical ones. Second we have considered the two-dimensional unsteady flow around a circular cylinder placed between two parallel solid walls and compared the results with those of the database of the Priority Research Program ‘Flow Simulation on High Performance Computers’ of the German Research Association (DFG). Third, we have considered the two-dimensional flow within a \(S\)-shaped duct containing an elliptical valve. Finally, we have applied the technique to the study of a practical high-Reynolds number industrial problem. From the Summary