Open Access
Issue
ESAIM: M2AN
Volume 56, Number 2, March-April 2022
Page(s) 565 - 592
DOI https://doi.org/10.1051/m2an/2022016
Published online 28 February 2022
  1. E. Ahmed, J. Jaffré and J.E. Roberts, A reduced fracture model for two-phase flow with different rock types. Math. Comput. Simul. 137 (2017) 49–70. [CrossRef] [Google Scholar]
  2. C. Alboin, J. Jaffré, J.E. Roberts, X. Wang and C. Serres, Domain decomposition for some transmission problems in flow in porous media. In: Numerical Treatment of Multiphase Flows in Porous Media (Beijing, 1999). Vol. 552 of Lecture Notes in Phys. Springer, Berlin (2000) 22–34. [CrossRef] [Google Scholar]
  3. L. Amir, M. Kern, V. Martin and J.E. Roberts, Décomposition de domaine et préconditionnement pour un modèle 3D en milieu poreux fracturé In: Proceeding of JANO 8, 8t Conference on Numerical Analysis and Optimization (2005). [Google Scholar]
  4. P. Angot, Well-posed Stokes/Brinkman and Stokes/Darcy coupling revisited with new jump interface conditions. ESAIM: M2AN 52 (2018) 1875–1911. [CrossRef] [EDP Sciences] [Google Scholar]
  5. S.N. Antontsev and S.I. Shmarev, A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions. Nonlinear Anal. Theory Methods App. 60 (2005) 515–545. [CrossRef] [Google Scholar]
  6. J. Audu, F. Fairag and S. Messaoudi, On the well-posedness of generalized Darcy-Forchheimer equation. Boundary Value Prob. 2018 (2018) 1–17. [CrossRef] [Google Scholar]
  7. C. Bernardi, F. Hecht and O. Pironneau, Coupling Darcy and Stokes equations for porous media with cracks. ESAIM: M2AN 39 (2005) 7–35. [CrossRef] [EDP Sciences] [Google Scholar]
  8. S. Berrone, S. Pieraccini and S. Scialò, A PDE-constrained optimization formulation for discrete fracture network flows. SIAM J. Sci. Comput. 35 (2013) B487–B510. [Google Scholar]
  9. S. Berrone, S. Pieraccini and S. Scialò, On simulations of discrete fracture network flows with an optimization-based extended finite element method. SIAM J. Sci. Comput. 35 (2013) 908–935. [Google Scholar]
  10. D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics. Springer, Berlin, Heidelberg, 2013. [CrossRef] [Google Scholar]
  11. J.W. Both, J.M. Nordbotten and F.A. Radu, Free energy diminishing discretization of darcy-forchheimer flow in poroelastic media. In: Finite Volumes for Complex Applications IX – Methods, Theoretical Aspects, Examples, edited by R. Klöfkorn, E. Keilegavlen, F.A. Radu and J. Fuhrmann. Springer International Publishing, Cham, (2020) 203–211. [CrossRef] [Google Scholar]
  12. M. Bulíček, J. Málek and J. Žabenský, A generalization of the Darcy-Forchheimer equation involving an implicit, pressure-dependent relation between the drag force and the velocity. J. Math. Anal. App. 424 (2015) 785–801. [CrossRef] [Google Scholar]
  13. C. Cancès, Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities. ESAIM: M2AN 43 (2009) 973–1001. [CrossRef] [EDP Sciences] [Google Scholar]
  14. B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson and A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Adv. Water Res. 111 (2018) 239–258. [CrossRef] [Google Scholar]
  15. L. Formaggia, A. Fumagalli, A. Scotti and P. Ruffo, A reduced model for Darcy’s problem in networks of fractures. ESAIM: M2AN 48 (2014) 1089–1116. [CrossRef] [EDP Sciences] [Google Scholar]
  16. N. Frih, J.E. Roberts and A. Saada, Modeling fractures as interfaces: a model for Forchheimer fractures. Comput. Geosci. 12 (2008) 91–104. [CrossRef] [MathSciNet] [Google Scholar]
  17. C. Geuzaine and J.-F. Remacle, Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79 (2009) 1309–1331. [CrossRef] [Google Scholar]
  18. R. Granero-Belinchón and S. Shkoller, Well-posedness and decay to equilibrium for the Muskat problem with discontinuous permeability. Trans. Am. Math. Soc. 372 (2019) 2255–2286. [CrossRef] [Google Scholar]
  19. C. Johannes van Duijn, H. Eichel, R. Helmig and I.S. Pop, Effective equations for two-phase flow in porous media: the effect of trapping on the microscale. Transp. Porous Media 69 (2007) 411–428. [CrossRef] [MathSciNet] [Google Scholar]
  20. E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela and I. Berre, Porepy: an open-source software for simulation of multiphysics processes in fractured porous media. Comput. Geosci. 25 (2021) 243–265. [CrossRef] [MathSciNet] [Google Scholar]
  21. P. Knabner and J.E. Roberts, Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture. ESAIM: M2AN 48 (2014) 1451–1472. [CrossRef] [EDP Sciences] [Google Scholar]
  22. K. Kumar, F. List, I.S. Pop and F.A. Radu, Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. J. Comput. Phys. 407 (2020) 109138. [CrossRef] [MathSciNet] [Google Scholar]
  23. F. List and F.A. Radu, A study on iterative methods for solving Richards’ equation. Comput. Geosci. 20 (2016) 341–353. [Google Scholar]
  24. V. Martin, J. Jaffré and J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM J. Sci. Comput. 26 (2005) 1667–1691. [Google Scholar]
  25. F.A. Morales and R.E. Showalter, A Darcy-Brinkman model of fractures in porous media. J. Math. Anal. App. 452 (2017) 1332–1358. [CrossRef] [Google Scholar]
  26. J.T. Oden and J.N. Reddy, Variational Methods in Theoretical Mechanics. Springer, Berlin Heidelberg (1976). [CrossRef] [Google Scholar]
  27. M.A. Peletier, Variational modelling: energies, gradient flows, and large deviations. Preprint arXiv:1402.1990 (2014). [Google Scholar]
  28. I.S. Pop, F. Radu and P. Knabner, Mixed finite elements for the Richards’ equation: linearization procedure. J. Comput. Appl. Math. 168 (2004) 365–373. [CrossRef] [MathSciNet] [Google Scholar]
  29. F.A. Radu, K. Kumar, J.M. Nordbotten and I.S. Pop, A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities. IMA J. Numer. Anal. 38 (2017) 884–920. [Google Scholar]
  30. P.-A. Raviart and J.-M. Thomas, A mixed finite element method for second order elliptic problems. Lecture Notes Math. 606 (1977) 292–315. [CrossRef] [Google Scholar]
  31. J.E. Roberts and J.-M. Thomas, Mixed and hybrid methods. In: Handbook of Numerical Analysis. Vol. II, Handb. Numer. Anal., II. North-Holland, Amsterdam (1991) 523–639. [Google Scholar]
  32. I. Rybak and S. Metzger, A dimensionally reduced stokes-Darcy model for fluid flow in fractured porous media. App. Math. Comput. 384 (2020) 125260. [CrossRef] [Google Scholar]
  33. J.J. Salas, H. López and B. Molina, An analysis of a mixed finite element method for a Darcy-Forchheimer model. Math. Comput. Modell. 57 (2013) 2325–2338. [CrossRef] [Google Scholar]
  34. F. Spena and A. Vacca, A potential formulation of non-linear models of flow through anisotropic porous media. Transp. Porous Media 45 (2001) 405–421. [CrossRef] [Google Scholar]
  35. J.L. Vazquez, The Porous Medium Equation. Oxford University Press (2006). [CrossRef] [Google Scholar]
  36. Z. Zeng and R. Grigg, A criterion for non-Darcy flow in porous media. Transp. Porous Media 63 (2006) 57–69. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you