A block-centered finite difference method for an unsteady asymptotic coupled model in fractured media aquifer system

Abstract A block-centered finite difference method is proposed for solving an unsteady asymptotic coupled model, in which the flow is governed by Darcy’s law both in the one-dimensional fracture and two-dimensional porous media. The second-order error estimates in discrete norms are derived on nonuniform rectangular grids for both pressure and velocity. The numerical scheme can be extended to nonmatching spatial and temporal grids without loss of accuracy. Numerical experiments are performed to verify the efficiency and accuracy of the proposed method. It is shown that the pressure and velocity are discontinuous across the fracture-interface and the fracture indeed acts as the fast pathway or geological barrier in the aquifer system.

[1]  Philippe Angot,et al.  ASYMPTOTIC AND NUMERICAL MODELLING OF FLOWS IN FRACTURED POROUS MEDIA , 2009 .

[2]  Alfio Quarteroni,et al.  A multiscale Darcy–Brinkman model for fluid flow in fractured porous media , 2011, Numerische Mathematik.

[3]  Hongxing Rui,et al.  A Block-Centered Finite Difference Method for the Darcy-Forchheimer Model , 2012, SIAM J. Numer. Anal..

[4]  A. Weiser,et al.  On convergence of block-centered finite differences for elliptic-problems , 1988 .

[5]  Wei Liu,et al.  A Two-Grid Block-Centered Finite Difference Method For Darcy-Forchheimer Flow in Porous Media , 2015, SIAM J. Numer. Anal..

[6]  Alessio Fumagalli,et al.  Numerical modelling of multiphase subsurface flow in the presence of fractures , 2011 .

[7]  Fernando A. Morales,et al.  The narrow fracture approximation by channeled flow , 2010 .

[8]  Mary F. Wheeler,et al.  A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra , 2011, Numerische Mathematik.

[9]  Xiaoming Wang,et al.  On the coupled continuum pipe flow model (CCPF) for flows in karst aquifer , 2009 .

[10]  Yanzhao Cao,et al.  Analysis and finite element approximation of a coupled, continuum pipe‐flow/Darcy model for flow in porous media with embedded conduits , 2011 .

[11]  Hongxing Rui,et al.  A block‐centered finite difference method for Darcy–Forchheimer model with variable Forchheimer number , 2015 .

[12]  Georg Teutsch,et al.  Simulation of the development of karst aquifers using a coupled continuum pipe flow model , 2003 .

[13]  Wei Liu,et al.  Anisotropic Wilson element with conforming finite element approximation for a coupled continuum pipe‐flow/Darcy model in Karst aquifers , 2015 .

[14]  Gilberto Espinosa-Paredes,et al.  Analytical Analysis for Mass Transfer in a Fractured Porous Medium , 2013 .

[15]  M. Wheeler.  A Priori L_2 Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations , 1973 .

[16]  Dan Ma,et al.  Numerical study on seepage property of karst collapsecolumns under particle migration , 2013 .

[17]  Vincent Martin,et al.  Modeling Fractures and Barriers as Interfaces for Flow in Porous Media , 2005, SIAM J. Sci. Comput..

[18]  Sebastian Bauer,et al.  Modeling of karst aquifer genesis: Influence of exchange flow , 2003 .

[19]  Mary F. Wheeler,et al.  A Multipoint Flux Mixed Finite Element Method , 2006, SIAM J. Numer. Anal..

[20]  Wei Liu,et al.  A new nonconforming finite element with a conforming finite element approximation for a coupled continuum pipe‐flow/Darcy model in Karst aquifers , 2016 .

[21]  Jean E. Roberts,et al.  Space-time Domain Decomposition and Mixed Formulation for solving reduced fracture models , 2015 .

[22]  Vincent Martin,et al.  Modeling fractures as interfaces with nonmatching grids , 2012, Computational Geosciences.

[23]  Georg Teutsch,et al.  Hydraulic boundary conditions as a controlling factor in karst genesis: A numerical modeling study on artesian conduit development in gypsum , 2003 .

[24]  D. Loper,et al.  An analytic benchmark test for karst-aquifer flow , 2013 .

[25]  Wei Liu,et al.  Finite volume element approximation of the coupled continuum pipe‐flow/Darcy model for flows in karst aquifers , 2014 .

[26]  Wenbin Chen,et al.  Adjoint method for an inverse problem of CCPF model , 2014 .