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Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy–Forchheimer flow in the fracture

Peter KnabnerJean E. Roberts — 2014

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy−Forchheimerlaw while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy−Forchheimerlaw is the governing equation throughout the domain. We show existence and uniqueness of the solution...

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