Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities
ESAIM: M2AN, 43 5 (2009) 973-1001
Published online: 2009-08-01
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Numerical investigations on the performance of sc-CO2 sequestration in heterogeneous deep saline aquifers under non-isothermal conditions
Tummuri Naga Venkata Pavan, Srinivasa Reddy Devarapu and Suresh Kumar GovindarajanGas Science and Engineering 130 205437 (2024)
https://doi.org/10.1016/j.jgsce.2024.205437
EURAD state-of-the-art report: development and improvement of numerical methods and tools for modeling coupled processes in the field of nuclear waste disposal
F. Claret, N. I. Prasianakis, A. Baksay, D. Lukin, G. Pepin, E. Ahusborde, B. Amaziane, G. Bátor, D. Becker, A. Bednár, M. Béreš, S. Bérešová, Z. Böthi, V. Brendler, K. Brenner, J. Březina, F. Chave, S. V. Churakov, M. Hokr, D. Horák, D. Jacques, F. Jankovský, C. Kazymyrenko, T. Koudelka, T. Kovács, et al.Frontiers in Nuclear Engineering 3 (2024)
https://doi.org/10.3389/fnuen.2024.1437714
Convergent sequential fully implicit method for reservoir simulation
S.H. Lee, P. Tomin and Y. EfendievJournal of Computational Physics 492 112442 (2023)
https://doi.org/10.1016/j.jcp.2023.112442
Studying the features of simulating fluid movement in porous media
K. M. Shiyapov, Zh. D. Baishemirov, Zh. A. Abdiramanov and A. B. ZhanbyrbayevHerald of the Kazakh-British technical university 20 (4) 63 (2023)
https://doi.org/10.55452/1998-6688-2023-20-4-63-71
Sequential implicit vertex approximate gradient discretization of incompressible two-phase Darcy flows with discontinuous capillary pressure
K. Brenner, N. Chorfi and R. MassonComputational Geosciences 26 (1) 147 (2022)
https://doi.org/10.1007/s10596-021-10113-7
Model adaptation for non-linear elliptic equations in mixed form: existence of solutions and numerical strategies
Alessio Fumagalli and Francesco Saverio PatacchiniESAIM: Mathematical Modelling and Numerical Analysis 56 (2) 565 (2022)
https://doi.org/10.1051/m2an/2022016
On several numerical strategies to solve Richards’ equation in heterogeneous media with finite volumes
Sabrina Bassetto, Clément Cancès, Guillaume Enchéry and Quang-Huy TranComputational Geosciences 26 (5) 1297 (2022)
https://doi.org/10.1007/s10596-022-10150-w
Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure
K Brenner, R Masson, E H Quenjel and J DroniouIMA Journal of Numerical Analysis 42 (2) 1231 (2022)
https://doi.org/10.1093/imanum/drab018
A Gravity Current Model with Capillary Trapping for Oil Migration in Multilayer Geological Basins
Clément Cancès and David MalteseSIAM Journal on Applied Mathematics 81 (2) 454 (2021)
https://doi.org/10.1137/19M1284233
Polyhedral Methods in Geosciences
Konstantin Brenner, Julian Hennicker and Roland MassonSEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 73 (2021)
https://doi.org/10.1007/978-3-030-69363-3_3
Finite-volume simulation of capillary-dominated flow in matrix-fracture systems using interface conditions
Ammar H. Alali, François P. Hamon, Bradley T. Mallison and Hamdi A. TchelepiComputational Geosciences 25 (1) 17 (2021)
https://doi.org/10.1007/s10596-020-09982-1
Upstream mobility finite volumes for the Richards equation in heterogenous domains
Sabrina Bassetto, Clément Cancès, Guillaume Enchéry and Quang-Huy TranESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2101 (2021)
https://doi.org/10.1051/m2an/2021047
A discrete fracture model for two-phase flow involving the capillary pressure discontinuities in fractured porous media
Xiao-Hong Wang, Lu Li, Min Wang, Zhi-Feng Liu and An-Feng ShiAdvances in Water Resources 142 103607 (2020)
https://doi.org/10.1016/j.advwatres.2020.103607
Space–time domain decomposition for two-phase flow between different rock types
Elyes Ahmed, Caroline Japhet and Michel KernComputer Methods in Applied Mechanics and Engineering 371 113294 (2020)
https://doi.org/10.1016/j.cma.2020.113294
Simulation of two-phase flow in porous media with sharp material discontinuities
L.K. Tran, J.C. Kim and S.K. MatthäiAdvances in Water Resources 142 103636 (2020)
https://doi.org/10.1016/j.advwatres.2020.103636
Vertex Approximate Gradient discretization preserving positivity for two-phase Darcy flows in heterogeneous porous media
K. Brenner, R. Masson and E.H. QuenjelJournal of Computational Physics 409 109357 (2020)
https://doi.org/10.1016/j.jcp.2020.109357
(2019)
https://doi.org/10.2118/193886-MS
Splitting-based domain decomposition methods for two-phase flow with different rock types
Elyes AhmedAdvances in Water Resources 134 103431 (2019)
https://doi.org/10.1016/j.advwatres.2019.103431
A Cell-Centred CVD-MPFA Finite Volume Method for Two-Phase Fluid Flow Problems with Capillary Heterogeneity and Discontinuity
Raheel Ahmed, Yawei Xie and Michael G. EdwardsTransport in Porous Media 127 (1) 35 (2019)
https://doi.org/10.1007/s11242-018-1179-y
Hybrid discretization of multi-phase flow in porous media in the presence of viscous, gravitational, and capillary forces
S. H. Lee and Y. EfendievComputational Geosciences 22 (5) 1403 (2018)
https://doi.org/10.1007/s10596-018-9760-6
Implicit Hybrid Upwinding for two-phase flow in heterogeneous porous media with buoyancy and capillarity
François P. Hamon, Bradley T. Mallison and Hamdi A. TchelepiComputer Methods in Applied Mechanics and Engineering 331 701 (2018)
https://doi.org/10.1016/j.cma.2017.10.008
Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition
Iuliu Sorin Pop, Jeroen Bogers and Kundan KumarVietnam Journal of Mathematics 45 (1-2) 77 (2017)
https://doi.org/10.1007/s10013-016-0198-7
Numerical Analysis of a Robust Free Energy Diminishing Finite Volume Scheme for Parabolic Equations with Gradient Structure
Clément Cancès and Cindy GuichardFoundations of Computational Mathematics 17 (6) 1525 (2017)
https://doi.org/10.1007/s10208-016-9328-6
Modeling two-phase flow of immiscible fluids in porous media: Buckley-Leverett theory with explicit coupling terms
Sylvain Pasquier, Michel Quintard and Yohan DavitPhysical Review Fluids 2 (10) (2017)
https://doi.org/10.1103/PhysRevFluids.2.104101
Nonlinear analysis of multiphase transport in porous media in the presence of viscous, buoyancy, and capillary forces
Boxiao Li and Hamdi A. TchelepiJournal of Computational Physics 297 104 (2015)
https://doi.org/10.1016/j.jcp.2015.04.057
Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media
K. Brenner, M. Groza, C. Guichard and R. MassonESAIM: Mathematical Modelling and Numerical Analysis 49 (2) 303 (2015)
https://doi.org/10.1051/m2an/2014034
Velocity Projection with Upwind Scheme Based on the Discontinuous Galerkin Methods for the Two Phase Flow Problem
Jiangyong Hou, Wenjing Yan and Jie ChenInternational Journal of Modern Nonlinear Theory and Application 04 (02) 127 (2015)
https://doi.org/10.4236/ijmnta.2015.42009
Influence of small-scale heterogeneity on upward CO2 plume migration in storage aquifers
Boxiao Li and Sally M. BensonAdvances in Water Resources 83 389 (2015)
https://doi.org/10.1016/j.advwatres.2015.07.010
On interface transmission conditions for conservation laws with discontinuous flux of general shape
Boris Andreianov and Clément CancèsJournal of Hyperbolic Differential Equations 12 (02) 343 (2015)
https://doi.org/10.1142/S0219891615500101
A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
Peter BastianComputational Geosciences 18 (5) 779 (2014)
https://doi.org/10.1007/s10596-014-9426-y
A computational model for fluid leakage in heterogeneous layered porous media
Mehdi Musivand Arzanfudi, Rafid Al-Khoury and Lambertus J. SluysAdvances in Water Resources 73 214 (2014)
https://doi.org/10.1016/j.advwatres.2014.08.016
Approximating the vanishing capillarity limit of two‐phase flow in multi‐dimensional heterogeneous porous medium
B. Andreianov, K. Brenner and C. CancèsZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 94 (7-8) 655 (2014)
https://doi.org/10.1002/zamm.201200218
Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation
R. Eymard, C. Guichard, R. Herbin and R. MassonZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 94 (7-8) 560 (2014)
https://doi.org/10.1002/zamm.201200206
Results of the MoMaS benchmark for gas phase appearance and disappearance using generalized MHFE
E. Marchand and P. KnabnerAdvances in Water Resources 73 74 (2014)
https://doi.org/10.1016/j.advwatres.2014.07.005
A phase-by-phase upstream scheme that converges to the vanishing capillarity solution for countercurrent two-phase flow in two-rock media
Boris Andreianov and Clément CancèsComputational Geosciences 18 (2) 211 (2014)
https://doi.org/10.1007/s10596-014-9403-5
Unconditionally Convergent Nonlinear Solver for Multiphase Flow in Porous Media under Viscous Force, Buoyancy, and Capillarity
Boxiao Li and Hamdi A. TchelepiEnergy Procedia 59 404 (2014)
https://doi.org/10.1016/j.egypro.2014.10.395
A family of steady two-phase generalized Forchheimer flows and their linear stability analysis
Luan T. Hoang, Akif Ibragimov and Thinh T. KieuJournal of Mathematical Physics 55 (12) (2014)
https://doi.org/10.1063/1.4903002
Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure
Konstantin Brenner, Clément Cancès and Danielle HilhorstComputational Geosciences 17 (3) 573 (2013)
https://doi.org/10.1007/s10596-013-9345-3
Vanishing capillarity solutions of Buckley–Leverett equation with gravity in two-rocks’ medium
Boris Andreianov and Clément CancèsComputational Geosciences 17 (3) 551 (2013)
https://doi.org/10.1007/s10596-012-9329-8
Trust-region based solver for nonlinear transport in heterogeneous porous media
Xiaochen Wang and Hamdi A. TchelepiJournal of Computational Physics 253 114 (2013)
https://doi.org/10.1016/j.jcp.2013.06.041
Numerical simulation of two-phase immiscible incompressible flows in heterogeneous porous media with capillary barriers
I. Mozolevski and L. SchuhJournal of Computational and Applied Mathematics 242 12 (2013)
https://doi.org/10.1016/j.cam.2012.09.045
(2013)
https://doi.org/10.2118/163600-MS
Numerical simulations of water–gas flow in heterogeneous porous media with discontinuous capillary pressures by the concept of global pressure
Brahim Amaziane, Mladen Jurak and Ana Žgaljić KekoJournal of Computational and Applied Mathematics 236 (17) 4227 (2012)
https://doi.org/10.1016/j.cam.2012.05.013
An Existence Result for Multidimensional Immiscible Two-Phase Flows with Discontinuous Capillary Pressure Field
Clément Cancès and Michel PierreSIAM Journal on Mathematical Analysis 44 (2) 966 (2012)
https://doi.org/10.1137/11082943X
Numerical simulation of gas migration through engineered and geological barriers for a deep repository for radioactive waste
Brahim Amaziane, Mustapha El Ossmani and Mladen JurakComputing and Visualization in Science 15 (1) 3 (2012)
https://doi.org/10.1007/s00791-013-0196-1
Finite Volumes for Complex Applications VI Problems & Perspectives
K. Brenner, C. Cancès and D. HilhorstSpringer Proceedings in Mathematics, Finite Volumes for Complex Applications VI Problems & Perspectives 4 185 (2011)
https://doi.org/10.1007/978-3-642-20671-9_20
Asymptotic Behavior of Two-Phase Flows in Heterogeneous Porous Media for Capillarity Depending Only on Space. II. Nonclassical Shocks to Model Oil-Trapping
Clément CancèsSIAM Journal on Mathematical Analysis 42 (2) 972 (2010)
https://doi.org/10.1137/090747993
Asymptotic Behavior of Two-Phase Flows in Heterogeneous Porous Media for Capillarity Depending Only on Space. I. Convergence to the Optimal Entropy Solution
Clément CancèsSIAM Journal on Mathematical Analysis 42 (2) 946 (2010)
https://doi.org/10.1137/090747981
Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures
A. Ern, I. Mozolevski and L. SchuhComputer Methods in Applied Mechanics and Engineering 199 (23-24) 1491 (2010)
https://doi.org/10.1016/j.cma.2009.12.014