Section: New Results

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

C. Cancès, T. O. Gallouët, M. Laborde, L. Monsaingeon. In [6]: the Wasserstein gradient flow structure of the PDE system governing multiphase flows in porous media was recently highlighted in [68]. The model can thus be approximated by means of the minimizing movement (or JKO) scheme. We solve the JKO scheme using the ALG2-JKO scheme proposed in [2]. The numerical results are compared to a classical upstream mobility Finite Volume scheme, for which strong stability properties can be established.