Numerical Approach of a Water Flow in an Unsaturated Porous Medium by Coupling Between the Navier–Stokes and Darcy–Forchheimer Equations

1. Beavers, G.S., & Joseph, D.D. (1967). Boundary conditions at naturally permeable wall. Journal of Fluid Mechanics, 30(1), 197–207.10.1017/S0022112067001375Open DOISearch in Google Scholar

2. Saffman, P.G. (1971). On the boundary condition at the surface of a porous medium. Studies in Applied Mathematics, 50(2), 93–101.10.1002/sapm197150293Open DOISearch in Google Scholar

3. Correa, M.R., & Loula, A.F.D. (2009). A unified mixed formulation naturally coupling Stokes and Darcy flows. Computer Methods in Applied Mechanics and Engineering, 198(33-36), 2710–2722.10.1016/j.cma.2009.03.016Search in Google Scholar

4. Urquiza, J.M., N’Dri, D., Garon A., & Delfour, M.C. (2008). Coupling Stokes and Darcy equations. Applied Numerical Mathematics, 58(5), 525–538.10.1016/j.apnum.2006.12.006Search in Google Scholar

5. Pacquaut, G., Bruchon, J., Moulin N., & Drapier, S. (2011). Combining a level-set method and a mixed stabilized P1/P1 formulation for coupling Stokes-Darcy flows. International Journal for Numerical Methods in Fluids, 66.Search in Google Scholar

6. Gatica, G.N., Oyarzúa, R., & Sayas, F.-J. (2011). Convergence of a family of Galerkin discretizations for the Stokes-Darcy coupled problem. Numerical Methods for Partial Differential Equations, 27(3), 721–748.10.1002/num.20548Search in Google Scholar

7. Masud, A. (2007). A stabilized mixed finite element method for Darcy-Stokes flow. International Journal for Numerical Methods in Fluids, 54(6–8), 665–681.10.1002/fld.1508Open DOISearch in Google Scholar

8. Tan, H., & Pillai, K. M. (2009). Finite element implementation of stress-jump and stress-continuity conditions at porous-medium, clear-fluid interface. Computers & Fluids, 38(6), 1118–1131.10.1016/j.compfluid.2008.11.006Search in Google Scholar

9. Arquis, E., & Caltagirone, J.P. (1984). Sur les conditions hydrodynamiques au voisinage d’une interface milieu _uide-milieu poreux : application à la convection naturelle. Comptes Rendus de l’Académie des Science de Paris, Série II, 299, 1–4.Search in Google Scholar

10. Arquis, E., Caltagirone, J.P., & Le Breton, P. (1991). Détermination des propriétés de dispersion d’un milieu périodique à partir de l’analyse locale des transferts thermiques. Comptes Rendus de l’Académie des Science de Paris, Série II, 313, 1087–1092.Search in Google Scholar

11. Vincent, S., Caltagirone, J.-P., Lubin, P., & Randrianarivelo, T.-N. (2004). An adaptative augmented lagrangian method for three-dimensional multimaterial flows. Computers & Fluids, 33, 1273–1289.10.1016/j.compfluid.2004.01.002Search in Google Scholar

12. Randrianarivelo, T.N., Pianet, G., Vincent S., & Caltagirone, J.-P. (2005). Numerical modelling of solid particle motion using a new penalty method. International Journal for Numerical Methods in Fluids, 47, 1245–1251.10.1002/fld.914Open DOISearch in Google Scholar

13. Sarthou, A., Vincent, S., Caltagirone, J.-P., & Angot, P. (2008). Eulerian lagrangian grid coupling and penalty methods for the simulation of multiphase flows interacting with complex objects. International Journal for Numerical Methods in Fluids, 56, 1093–1099.10.1002/fld.1661Open DOISearch in Google Scholar

14. Puaux, G. (2011). Numerical simulation of flows at microscopic and mesoscopic scales in RTM process. PhD thesis. École nationale supérieure des mines de Paris.Search in Google Scholar

15. Patankar, S.V. (1980). Numerical Heat Transfer and Fluid Flow. Hémisphère Inc.: McGraw-Hill, Washington, États-Unis.Search in Google Scholar

16. Versteeg, H.K, & Malalasekera, W. (1995). Introduction to Computational Fluid Dynamics: The Finite Volume Method. Wiley, New York, États-Unis.Search in Google Scholar

17. Bear, J. (1972). Dynamics of fluids in porous media. Elsevier.Search in Google Scholar