Simulation of multiphase porous media flows with minimising movement and finite volume schemes

Multiphase porous media flows; Wasserstein gradient flow; Constrained optimization; Finite volume method; Lagrange multipliers; Stability; Augmented Lagrangian methods; Finite volume schemes; Flows in porous media; Gradient flow; Multiphase porous media; Numerical results; Partial differential; Porous materials

Abstract :

[en] The Wasserstein gradient flow structure of the partial differential equation system governing multiphase flows in porous media was recently highlighted in Cancès et al. [Anal. PDE 10(8), 1845-1876]. The model can thus be approximated by means of the minimising movement (or JKO after Jordan, Kinderlehrer and Otto [SIAM J. Math. Anal. 29(1), 1-17]) scheme that we solve thanks to the ALG2-JKO scheme proposed in Benamou et al. [ESAIM Proc. Surv. 57, 1-17]. The numerical results are compared to a classical upstream mobility finite volume scheme, for which strong stability properties can be established. © Cambridge University Press 2018.

Disciplines :

Mathematics

Author, co-author :

Cancès, C.; Inria, Univ. Lille, CNRS, UMR 8524, Laboratoire Paul Painlevé, Lille, F-59000, France

Gallouët, Thomas ; Université de Liège - ULg

Laborde, M.; Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada

Monsaingeon, L.; IECL, Université de Lorraine, Nancy, France, GFM, Universidade de Lisboa, Lisbon, Portugal

Language :

English

Title :

Simulation of multiphase porous media flows with minimising movement and finite volume schemes

Publication date :

2019

Journal title :

European Journal of Applied Mathematics

ISSN :

0956-7925

eISSN :

1469-4425

Publisher :

Cambridge University Press, Cambridge, United Kingdom

Volume :

Issue :

Pages :

1123-1152

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

Institut national de la recherche scientifique, INRS; Agence Nationale de la Recherche, ANR
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 14 December 2021

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Bibliography

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