Analysis and finite element approximation of a coupled, continuum pipe‐flow/Darcy model for flow in porous media with embedded conduits

We consider the continuum Darcy/pipe flow model for flows in a porous matrix containing embedded conduits; such coupled flows are present in, e.g., karst aquifers. The mathematical well‐posedness of the coupled problem as well as convergence rates of finite element approximation are established in the two‐dimensional case. Computational results are also provided. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1242–1252, 2011

[1]  M. Gunzburger,et al.  Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition , 2010 .

[2]  Jinchao Xu,et al.  A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow , 2007, SIAM J. Numer. Anal..

[3]  A. Quarteroni,et al.  Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations , 2004 .

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

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

[6]  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 .

[7]  E. Miglio,et al.  Mathematical and numerical models for coupling surface and groundwater flows , 2002 .

[8]  Thomas R. Gatliffe,et al.  Calibration and Reliability in Groundwater Modelling: Coping with Uncertainty , 2002, Technometrics.

[9]  E. Sudicky,et al.  Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media , 1996 .

[10]  E. Sudicky,et al.  On the Incorporation of Drains into Three‐Dimensional Variably Saturated Groundwater Flow Models , 1996 .

[11]  T. N. Narasimhan,et al.  Multidimensional numerical simulation of fluid flow in fractured porous media , 1982 .

[12]  G. Burton.  Sobolev Spaces , 2013 .

[13]  W. Marsden.  I and J , 2012 .

[14]  Weidong Zhao,et al.  Finite Element Approximations for Stokes–darcy Flow with Beavers–joseph Interface Conditions * , 2022 .

[15]  Olaf Kolditz,et al.  Calibration and Reliability in Groundwater Modelling , 2006 .

[16]  A. W. Harbaugh.  MODFLOW-2005 : the U.S. Geological Survey modular ground-water model--the ground-water flow process , 2005 .

[17]  Sebastian Bauer,et al.  Modelling of karst development considering conduit-matrix exchange flow , 2000 .

[18]  G. Teutsch,et al.  A combined continuum and discrete network reactive transport model for the simulation of karst development , 1996 .

[19]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[20]  Elemer Bobok,et al.  Fluid mechanics for petroleum engineers , 1993 .

[21]  M. Sauter.  Quantification and forecasting of regional groundwater flow and transport in a karst aquifer (Gallusquelle, Malm, SW. Germany) , 1992 .

[22]  W. Hongtao,et al.  Dual-media flow models of karst areas and their application in north China , 1988 .

[23]  B. Ji,et al.  The media and movement of karst water , 1988 .

[24]  J. Bear,et al.  Modeling groundwater flow and pollution , 1987 .

[25]  P. Grisvard.  Elliptic Problems in Nonsmooth Domains , 1985 .

[26]  J. Lions,et al.  Problèmes aux limites non homogènes et applications , 1968 .

[27]  G. I. Barenblatt,et al.  Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata] , 1960 .