Monolithic approach of Stokes-Darcy coupling for LCM process modelling

Lara Abouorm (1, 2, 3) , Nicolas Moulin (1, 2, 3) , Julien Bruchon (1, 3) , Sylvain Drapier (1, 2, 3)

1 MPE-ENSMSE - Département Mécanique et Procédés d'Elaboration
2 SMS-ENSMSE - Centre Science des Matériaux et des Structures
3 LGF-ENSMSE - Laboratoire Georges Friedel

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.

Mots clés: Darcy; Stokes; composites; level set; stabilization; multi-scale method

Domaines: Sciences de l'ingénieur [physics]

Lara Abouorm, Nicolas Moulin, Julien Bruchon, Sylvain Drapier. Monolithic approach of Stokes-Darcy coupling for LCM process modelling. CURRENT STATE-OF-THE-ART ON MATERIAL FORMING: NUMERICAL AND EXPERIMENTAL APPROACHES AT DIFFERENT LENGTH-SCALES, PTS 1-3, 2013, 554-557, pp.447-455. ⟨10.4028/www.scientific.net/KEM.554-557.447⟩. ⟨emse-00959587⟩