Total-velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure
| Autor: | Jérôme Droniou, Roland Masson, Konstantin Brenner, El Houssaine Quenjel |
|---|---|
| Přispěvatelé: | COmplex Flows For Energy and Environment (COFFEE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), School of Mathematical Sciences [Clayton], Monash University [Clayton], COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-16-CE06-0009,CHARMS,Modèles de Réservoirs Quantitatifs pour les Systèmes Hydrothermaux Complexes(2016) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Finite volume method
Darcy's law Discretization Applied Mathematics General Mathematics Weak solution Degrees of freedom (physics and chemistry) Upwind scheme 010103 numerical & computational mathematics Mechanics 01 natural sciences 010101 applied mathematics Computational Mathematics Nonlinear system Flow (mathematics) 0101 mathematics [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics |
| Zdroj: | IMA Journal of Numerical Analysis IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2021, ⟨10.1093/imanum/drab018⟩ IMA Journal of Numerical Analysis, 2021, ⟨10.1093/imanum/drab018⟩ |
| ISSN: | 0272-4979 1464-3642 |
| DOI: | 10.1093/imanum/drab018⟩ |
| Popis: | This work proposes a finite volume scheme for two-phase Darcy flow in heterogeneous porous media with different rock types. The fully implicit discretization is based on cell-centered, as well as face-centered degrees of freedom in order to capture accurately the nonlinear transmission conditions at different rock type interfaces. These conditions play a major role in the flow dynamics. The scheme is formulated with natural physical unknowns, and the notion of global pressure is only introduced to analyze its stability and convergence. It combines a two-point flux approximation of the gradient normal fluxes with a Hybrid Upwinding approximation of the transport terms. The convergence of the scheme to a weak solution is established taking into account the discontinuous capillary pressure at different rock type interfaces and the degeneracy of the phase mobilities. Numerical experiments show the additional robustness of the proposed discretization compared with the classical Phase Potential Upwinding approach. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|