Simulation of multiphase porous media flows with minimizing movement and finite volume schemes
Numerical Analysis
2018-07-23 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1802.01321,
title = {Simulation of multiphase porous media flows with minimizing movement and finite volume schemes},
author = {Clément Cancès and Thomas O. Gallouët and Maxime Laborde and Léonard Monsaingeon},
journal= {arXiv preprint arXiv:1802.01321},
year = {2018}
}