The paper describes the dissipative and dispersive properties of a hybrid RANS-LES Cartesian method specifically designed to study complex three-dimensional viscous flows. A skew-symmetric convective operator is employed to low the influence of numerical dissipation and dispersion on the physical phenomena especially when solving highly separated flows. The main objective is to conserve not only momentum and energy but also their quadratic forms. In principle, this should enhance the correct evolution of the turbulent kinetic energy in the wake of bluff-bodies thus allowing a confident estimate of the relevant scales. Here an immersed boundary technique is coupled with a wall-model in order to make affordable the study of high Reynolds number flows. The first part of the results is dedicated to basic one- and two-dimensional studies aiming at evaluating the performance of the scheme at the interface between cells of different size. Indeed, the refined Cartesian meshes are characterized by a fixed cell-size ratio of two and accuracy issues can locally occur. Moreover, three-dimensional test-cases are carried out whose results are compared with solutions from body-conforming methods and experimental data when available.