A numerical study of a turbulent premixed flame stabilized by a stagnation flow is presented. Such a geometry has been chosen because it features most of the phenomena that are encountered in systems of practical interest such as the interaction between the flame and a solid wall and the presence of important streamlines curvature. This study is based on a full second-order modeling, namely a Bray-Moss-Libby combustion model associated with a low-Reynolds number Reynolds-stress turbulence model. With respect to the mean Row properties, it is shown that, along the symmetry axis and in a large part of the mean flame brush, the turbulent diffusion term plays a minor role in the balance of the mean progress variable equation except in a thin zone. Such a finding is of importance because it confirms the results of recent studies of the literature that are based on an asymptotic analysis of the flow structure on the symmetry axis. Thus, the present results give a clear proof of what was so far an hypothesis. Concerning the balance of the turbulent fluxes of mass, the dominant role played by the correlation with the mean pressure gradient is clearly put into evidence. Although the agreement with experimental results is fair enough to recommend the use of such a modeling for systems of practical interest, some improvements have to be brought in the modeling of the correlations between the pressure fluctuations and the gradients of both the velocity and the progress variable fluctuations. Indeed, such quantities are expected to play a leading role for such a flow geometry especially in situations where the mean flame brush is close to the solid wall.