This paper presents some aspects concerning the 2D RANS numerical modeling of a Darrieus cross flow marine turbine. Two main features of the modeling are studied. The first deals with the influence of the near wall grid density on the numerical results. Most of the available literature concerning the occurrence of stalling foils emphasizes the need for a fine grid mesh at wall fitting y+ around the unity or less at the first near wall cell center. Nevertheless, in the case of a Darrieus turbine, the influence of this parameter has not yet been studied precisely. In particular, the exact y+ specification is not known, and its influence either on the global turbine performance or on the local flow field, has not been outlined. The present work provides insight into the y+ influence in a 2D Darrieus turbine and deals with its maximum acceptable value. The second feature concerns the ability of a 2D modeling to represent, the actual 3D flow in the turbine. The power coefficients CP are compared to those obtained in the hydrodynamic LEGI tunnel on a small scale model. The experimental power coefficients are presented with their associated precision. The comparisons show a medium tip speed ratio range around the nominal point for which the instantaneous ratio of the experimental and numerical power coefficients is a constant significantly lower than 1 regardless of the azimuthal position of the blades. This constant ratio is thought to be representative of the tip and arm-blade junctions losses.