Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media

Claire Chainais-Hillairet 1, 2 Stella Krell 3, 4 Alexandre Mouton 2
1 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
4 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : In this paper, we prove the convergence of a discrete duality finite volume scheme for a system of partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration. We first establish some a priori estimates satisfied by the sequences of approximate solutions. Then, it yields the compactness of these sequences. Passing to the limit in the numerical scheme, we finally obtain that the limit of the sequence of approximate solutions is a weak solution to the problem under study.
Document type :
Journal articles
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00929823
Contributor : Claire Chainais-Hillairet <>
Submitted on : Thursday, January 16, 2014 - 4:28:48 PM
Last modification on : Friday, May 10, 2019 - 10:14:03 AM
Long-term archiving on : Saturday, April 8, 2017 - 3:06:24 PM

File

paper2conv_CKM2014.pdf
Files produced by the author(s)

Identifiers

Citation

Claire Chainais-Hillairet, Stella Krell, Alexandre Mouton. Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media. Numerical Methods for Partial Differential Equations, Wiley, 2014, pp.38. ⟨10.1002/num.21913⟩. ⟨hal-00929823⟩

Share

Metrics

Record views

808

Files downloads

340