Nonlinear finite volume discretization for transient diffusion problems on general meshes
| Autor: | 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), 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) |
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Finite volume method Applied Mathematics Duality (optimization) 010103 numerical & computational mathematics 01 natural sciences Stability (probability) 010101 applied mathematics Computational Mathematics Nonlinear system Compact space Convergence (routing) Applied mathematics Polygon mesh [MATH]Mathematics [math] 0101 mathematics Diffusion (business) Mathematics |
| Zdroj: | Applied Numerical Mathematics Applied Numerical Mathematics, Elsevier, 2021, 161, pp.148-168. ⟨10.1016/j.apnum.2020.11.001⟩ Applied Numerical Mathematics, 2021, 161, pp.148-168. ⟨10.1016/j.apnum.2020.11.001⟩ |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2020.11.001 |
| Popis: | International audience; A nonlinear discrete duality finite volume scheme is proposed for time-dependent diffusion equations. The model example is written in a new formulation giving rise to similar nonlinearities for both the diffusion and the potential functions. A natural finite volume discretization is built on this particular problem's structure. The fluxes are generically approximated thanks to a key fractional average. The point of this strategy is to promote coercivity and scheme's stability simultaneously. The existence of positive solutions is guaranteed. The theoretical convergence of the nonlinear scheme is established using practical compactness tools. Numerical results are performed in order to highlight the second order accuracy of the methodology and the positiveness of solutions on distorted meshes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect