Combining a level‐set method and a mixed stabilized P1/P1 formulation for coupling Stokes–Darcy flows

Abstract

SUMMARY The aim of this work is to focus on the Stokes–Darcy coupled problem in order to simulate numerically, with the finite element method, composite manufacturing processes based on liquid resin infusion. In this study, a macroscopic description is used. The computational domain can be divided into two non‐miscible sub‐domains: a purely fluid domain and a porous medium. In the purely fluid domain, the fluid flows according to the Stokes equations, while in the porous medium, the fluid flows into the preforms according to the Darcy equations. Specific conditions have to be considered on the fluid/porous medium interface. The corresponding weak formulation is obtained by summing up the variational forms of the Stokes and Darcy equations over the whole domain. It is solved by a mixed velocity/pressure finite element method. In the purely fluid domain, a first‐order mixed P1+/ P1 finite element is used. However, in the porous medium, the Ladysenskaya–Brezzi–Babuska stability condition is not satisfied, and a P1/P1 finite element is preferred. It is stabilized with the Hughes Variational Multiscale formulation. The originality of our approach is two fold. First, one single unstructured mesh is considered for the whole domain. Second, the interface between the purely fluid domain and the porous medium is represented by a level‐set function. The level‐set framework is also used to capture the resin flow front. At the end of this paper, numerical simulations of such manufacturing processes by resin infusion/injection are presented. Copyright © 2011 John Wiley & Sons, Ltd.