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Existence of solutions to a model of two-phase flow in porous media

by S. Mishra and G. M. Coclite and K. H. Karlsen and N. H. Risebro

(Report number 2011-06)

Abstract
We consider the flow of two-phases in a porous medium and propose a modied version of the fractional flow model for incompressible, two-phase flow based on a Helmholtz regularization of the Darcy phase velocities. We show the existence of global-in-time entropy solutions for this model with suitable assumptions on the boundary conditions. Numerical experiments demonstrating the approximation of the classical two-phase flow equations with the new model are presented.

Keywords:

@Techreport{MCKR11_105,
  author = {S. Mishra and G. M. Coclite and K. H. Karlsen and N. H. Risebro},
  title = {Existence of solutions to a model of two-phase flow in porous media},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-06.pdf },
  year = {2011}
}

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