Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy–Forchheimer flow in the fracture∗. (13th August 2014)

• Record Type: Journal Article
• Authors: Knabner, Peter; Roberts, Jean E.
• Is Part Of: Mathematical modelling and numerical analysis. Volume 48:Part 5(2014)
• Page Start: 1451
• Page End: 1472
• Publication Date: 2014-08-13
• Subjects: Flow in porous media, -- fractures, -- Darcy−Forchheimerflow, -- solvability, -- regularization, -- monotone operators; Numerical analysis -- Periodicals; Mathematical models -- Periodicals; 510
• DOI: 10.1051/m2an/2014003
• Languages: English
• ISSNs: 0764-583X

Abstract

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−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 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−Forchheimerlaw in the entire domain when the Forchheimer coefficient in the matrix tends toward zero.