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A Thermodynamically Consistent Modeling and Numerical Framework for Non‐Isothermal Incompressible Two‐Phase Flow in Porous Media: Entropy Stability and Energy Conservation
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Positivity-preserving DDFV scheme for compressible two-phase flow in porous media
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Convergence of a TPFA finite volume scheme for nonisothermal immiscible compressible two-phase flow in porous media
An energy stable, conservative and bounds‐preserving numerical method for thermodynamically consistent modeling of incompressible two‐phase flow in porous media with rock compressibility
Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes
Léo Agélas, Martin Schneider, Guillaume Enchéry and Bernd Flemisch IMA Journal of Numerical Analysis 42(1) 515 (2022) https://doi.org/10.1093/imanum/draa064
A convergent finite volume scheme for dissipation driven models with volume filling constraint
Global existence of weak solutions to unsaturated poroelasticity
Jakub Wiktor Both, Iuliu Sorin Pop and Ivan Yotov ESAIM: Mathematical Modelling and Numerical Analysis 55(6) 2849 (2021) https://doi.org/10.1051/m2an/2021063
Upstream mobility finite volumes for the Richards equation in heterogenous domains
Sabrina Bassetto, Clément Cancès, Guillaume Enchéry and Quang-Huy Tran ESAIM: Mathematical Modelling and Numerical Analysis 55(5) 2101 (2021) https://doi.org/10.1051/m2an/2021047
The Gradient Discretization Method for Slow and Fast Diffusion Porous Media Equations
Positivity-preserving finite volume scheme for compressible two-phase flows in anisotropic porous media: The densities are depending on the physical pressures
Simulation of multiphase porous media flows with minimising movement and finite volume schemes
CLÉMENT CANCÈS, THOMAS GALLOUËT, MAXIME LABORDE and LÉONARD MONSAINGEON European Journal of Applied Mathematics 30(6) 1123 (2019) https://doi.org/10.1017/S0956792518000633
Numerical analysis of a finite volume scheme for a seawater intrusion model with cross‐diffusion in an unconfined aquifer
A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities
Florin A Radu, Kundan Kumar, Jan M Nordbotten and Iuliu S Pop IMA Journal of Numerical Analysis 38(2) 884 (2018) https://doi.org/10.1093/imanum/drx032
Numerical analysis of a finite volume scheme for two incompressible phase flow with dynamic capillary pressure
Khaled Bouadjila, Abdelhafid Mokrane, Ali Samir Saad and Mazen Saad Computers & Mathematics with Applications 75(10) 3614 (2018) https://doi.org/10.1016/j.camwa.2018.02.021
Energy stable numerical methods for porous media flow type problems
Clément Cancès, A. Anciaux-Sedrakian and Q. H. Tran Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 73 78 (2018) https://doi.org/10.2516/ogst/2018067
Convergence of a positive nonlinear Control Volume Finite Element scheme for solving an anisotropic degenerate breast cancer development model
Houssein Nasser El Dine, Mazen Saad and Raafat Talhouk Mathematics in Industry, Progress in Industrial Mathematics at ECMI 2016 26 695 (2017) https://doi.org/10.1007/978-3-319-63082-3_104
Efficient C1-continuous phase-potential upwind (C1-PPU) schemes for coupled multiphase flow and transport with gravity
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects
Clément Cancès and Flore Nabet Springer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects 199 431 (2017) https://doi.org/10.1007/978-3-319-57397-7_36
Implicit Hybrid Upwind scheme for coupled multiphase flow and transport with buoyancy
François P. Hamon, Bradley T. Mallison and Hamdi A. Tchelepi Computer Methods in Applied Mechanics and Engineering 311 599 (2016) https://doi.org/10.1016/j.cma.2016.08.009
Analysis of Hybrid Upwinding for Fully-Implicit Simulation of Three-Phase Flow with Gravity
Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media
K. Brenner, M. Groza, C. Guichard and R. Masson ESAIM: Mathematical Modelling and Numerical Analysis 49(2) 303 (2015) https://doi.org/10.1051/m2an/2014034
Adaptive heterogeneous multiscale methods for immiscible two-phase flow in porous media
Study of a numerical scheme for miscible two‐phase flow in porous media
Robert Eymard and Veronika Schleper Numerical Methods for Partial Differential Equations 30(3) 723 (2014) https://doi.org/10.1002/num.21823
An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media
Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation
R. Eymard, C. Guichard, R. Herbin and R. Masson ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 94(7-8) 560 (2014) https://doi.org/10.1002/zamm.201200206
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS
Finite volume approximation of degenerate two‐phase flow model with unlimited air mobility
Boris Andreianov, Robert Eymard, Mustapha Ghilani and Nouzha Marhraoui Numerical Methods for Partial Differential Equations 29(2) 441 (2013) https://doi.org/10.1002/num.21715
Two-phase flow equations with outflow boundary conditions in the hydrophobic–hydrophilic case