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

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CGLM_preprint(1).pdf (5.250Mb)
Date
2019
Dewey
Analyse
Sujet
Augmented Lagrangian method; minimizing movement scheme; Wasserstein gradient flow; Multiphase porous media flows; Finite Volumes AMS subjects classification
Journal issue
European Journal of Applied Mathematics
Volume
30
Number
6
Publication date
2019
Article pages
1123-1152
Publisher
Cambridge University Press
DOI
http://dx.doi.org/10.1017/S0956792518000633
URI
https://basepub.dauphine.fr/handle/123456789/20357
Collections
  • CEREMADE : Publications
Metadata
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Author
Cancès, Clément
32 Laboratoire Paul Painlevé - UMR 8524 [LPP]
Gallouët, Thomas
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laborde, Maxime
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Monsaingeon, Léonard
39398 Grupo de Física Matemática - Group of Mathematical Physics [GFM]
211251 Institut Élie Cartan de Lorraine [IECL]
Type
Article accepté pour publication ou publié
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. PDE10(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.

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