The present contribution is devoted to developing robust finite element solutions for coupling flows in both purely fluid region, ruled by Stokes equations, and fibrous preform region governed by a Darcy's law. Particularly the cases of low permeability of preform, down to 10(-15) m(2), are of interest to model LCM processes. Flows are solved using mixed finite elements stabilized with a sub-grid scale stabilization technique (ASGS). A special attention is paid to the interface conditions, namely normal stress and velocity continuity and tangential velocity constraint similar to a Beaver-Joseph-Saffinan's condition. The originality of the model consists in using one single mesh to represents the Stokes and the Darcy sub-domains (monolithic approach). A level set context is used to represent Stokes-Darcy interface and to capture the moving flow front. It is shown that provided a very special attention is paid to the coupling conditions, very precise results can be obtained. This monolithic approach is now perfectly robust due to the introduction of the ASGS sub-grid scale stabilization and leads to perform 3D complex shapes for manufacturing process by resin infusion.