Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fractureReport as inadecuate




Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture - Download this document for free, or read online. Document in PDF available to download.

1 Department of Mathematics 2 POMDAPI - Environmental Modeling, Optimization and Programming Models Inria Paris-Rocquencourt

Abstract : 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-Forchheimer law 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-Forchheimer law is the governing equation throughout the domain. We show existence and uniqueness of the solution and show that the solution for the model with Darcy-s law in the matrix is the weak limit of solutions of the model with the Darcy-Forchheimer law in the entire domain when the Forchheimer coefficient in the matrix tends toward zero.

Keywords : fractures flow in porous media Darcy-Forchheimer flow solvability regularization monotone operators





Author: Peter Knabner - Jean Roberts -

Source: https://hal.archives-ouvertes.fr/



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