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arXiv · 1802.01321

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

Clément Cancès·Thomas O. Gallouët·Maxime Laborde·Léonard Monsaingeon
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Abstract

The Wasserstein gradient flow structure of the PDE system governing multiphase flows in porous media was recently highlighted in [C. Canc\`es, T. O. Gallou\"et, and L. Monsaingeon, {\it Anal. PDE} 10(8):1845--1876, 2017]. The model can thus be approximated by means of the minimizing movement (or JKO) scheme, that we solve thanks to the ALG2-JKO scheme proposed in [J.-D. Benamou, G. Carlier, and M. Laborde, {\it ESAIM Proc. Surveys}, 57:1--17, 2016]. 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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Clément Cancès, Thomas O. Gallouët, Maxime Laborde, Léonard Monsaingeon. 2018-02-05. Simulation of multiphase porous media flows with minimizing movement and finite volume schemes. https://arxiv.org/abs/1802.01321

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