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

Knabner P, Roberts JE (2014)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2014

Journal

Mathematical Modelling and Numerical Analysis EDP Sciences

Book Volume: 48

Pages Range: 1451-1472

Journal Issue: 5

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2014/2014_KnRoberts_MathemAnalysisOfDiscrFractModelCouplDarcyFlowInMatrixWthDarcyForchheimer

DOI: 10.1051/m2an/2014003

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. © 2014 EDP Sciences, SMAI.

Authors with CRIS profile

Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Institut national de Recherche en Informatique et en Automatique (INRIA) FR France (FR)

How to cite

APA:

Knabner, P., & Roberts, J.E. (2014). Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture. Mathematical Modelling and Numerical Analysis, 48(5), 1451-1472. https://doi.org/10.1051/m2an/2014003

MLA:

Knabner, Peter, and Jean E. Roberts. "Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture." Mathematical Modelling and Numerical Analysis 48.5 (2014): 1451-1472.

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