Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2014

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

Peter Knabner
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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.
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Dates and versions

hal-00945028 , version 1 (11-02-2014)

Identifiers

  • HAL Id : hal-00945028 , version 1

Cite

Jean E. Roberts, Peter Knabner. Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture. ESAIM: Mathematical Modelling and Numerical Analysis, 2014, pp.1451-1472. ⟨hal-00945028⟩
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