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

Cancès, Clément; Gallouët, Thomas; Laborde, Maxime; Monsaingeon, Léonard (2019), Simulation of multiphase porous media flows with minimizing movement and finite volume schemes, European Journal of Applied Mathematics, 30, 6, p. 1123-1152. 10.1017/S0956792518000633

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
European Journal of Applied Mathematics
Volume
30
Number
6
Publisher
Cambridge University Press
Pages
1123-1152
Publication identifier
Metadata
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Author(s)
Cancès, Clément cc
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Gallouët, Thomas
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laborde, Maxime
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Monsaingeon, Léonard
Grupo de Física Matemática - Group of Mathematical Physics [GFM]
Institut Élie Cartan de Lorraine [IECL]
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.
Subjects / Keywords
Augmented Lagrangian method; minimizing movement scheme; Wasserstein gradient flow; Multiphase porous media flows; Finite Volumes AMS subjects classification