Écoulements diphasiques en milieux poreux hétérogènes : modélisation et analyse des effets liés aux discontinuités de la pression capillaire.

TL;DRAbstract

We consider the flow of a fluid made of oil and water in a heterogeneous porous medium, which is supposed to be a apposition of several homogeneous isotropic porous media. We are interested in the phenomena occurring at the interfaces between the different sub-media, and particularly if the capillary pressure is discontinuous w.r.t. the space.<br />We first deal with the case where some compatibility relations ensure that the capillary pressure connect in a strong sense. We prove the existence and the uniqueness of the weak solution. The existence result is obtained by proving the convergence of a Finite Volume scheme, while the uniqueness proof is based on the doubling variable technique.<br />In the following chapter, we deal with the case where no compatibility relation holds, so a new frame for the connection of the pressures is defined, using monotonous graphs. The existence of a weak solution is proven in the multidimensional case, while an uniqueness result, based on a uniform b

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