Simulation of multiphase porous media flows with minimizing movement and finite volume schemes
This work provides a novel numerical approach for simulating multiphase flows in porous media, which is important for applications in hydrology and petroleum engineering.
The paper applies a minimizing movement (JKO) scheme to simulate multiphase porous media flows, leveraging the Wasserstein gradient flow structure. Numerical results are compared with a classical upstream mobility Finite Volume scheme, demonstrating the JKO scheme's effectiveness.
The Wasserstein gradient flow structure of the PDE system governing multiphase flows in porous media was recently highlighted in [C. Cancès, T. O. Gallouët, 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.