Skip to main content
SpringerLink
Log in
Book cover

Environmental Studies pp 149–170Cite as

Eulerian-Lagrangian Localized Adjoint Methods for Reactive Transport in Groundwater

  • Conference paper

  • 222 Accesses

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 79))

Abstract

In this paper, we present Eulerian-Lagrangian localized adjoint methods (ELLAM) to solve convection-diffusion-reaction equations governing contaminant transport in groundwater flowing through an adsorbing porous medium. These ELLAM schemes can treat various combinations of boundary conditions and conserve mass. Numerical results are presented to demonstrate the strong potential of ELLAM schemes.

This research was supported in part by ONR Contract No. 0014-88-K-0370, by NSF Grant No. DMS-8922865, by funding from the Institute for Scientific Computation at Texas A&M University, by DOE, DE-ACO5-840R21400, Martin Marietta, Subcontracts, SK965C and SK966V, by DEPSCoR 94 Grant, and by funding from the Norwegian Research Council for Science and Humanities.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.B. ALLEN III, G.A. BEHIE, AND J.A. TRANGENSTEIN, Multiphase flow in porous media, Lecture Notes in Engineering, Springer-Verlag, Berlin (1988).

    Google Scholar 

  2. J.W. BARRETT AND K.W. MORTON, Approximate symmetrization and Petrov-Galerkin methods for diffusion-convection problems, Comp. Meth. Appl. Mech. Engrg., 45 (1984), pp. 97–122.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. BROOKS AND T.J.R. HUGHES, Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comp. Meth. Appl. Mech. Engrg., 32 (1982), pp. 199–259.

    Article  MathSciNet  MATH  Google Scholar 

  4. M.A. CELIA, I. HERRERA, E.T. BOULOUTAS, AND J.S. KINDRED, A new numerical approach for the advective-diffusive transport equation, Numerical Methods for PDE’s, 5 (1989), pp. 203–226.

    MathSciNet  MATH  Google Scholar 

  5. M.A. CELIA, T.F. RUSSELL, I. HERRERA, AND R.E. EWING, An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation, Advances in Water Resources, 13 (1990), pp. 187–206.

    Article  Google Scholar 

  6. M.A. CELIA AND S. ZISMAN, An Eulerian-Lagrangian localized adjoint method for reactive transport in groundwater, Computational Methods in Subsurface Hydrology, Proceedings of the Eighth International Conference on Computational Methods in Water Resources, Venice, Italy (1990), pp. 383–392.

    Google Scholar 

  7. H.K. DAHLE, M.S. ESPEDAL, AND R.E. EWING, Characteristic Petrov-Galerkin subdomain methods for convection diffusion problems (M.F. Wheeler, ed.), IMA Volume 11, Numerical Simulation in Oil Recovery, Springer-Verlag, Berlin (1988), pp. 77–88.

    Google Scholar 

  8. H.K. DAHLE, M.S. ESPEDAL, R.E. EWING, AND O. SEVAREID, Characteristic adaptive sub-domain methods for reservoir flow problems, Numerical Methods for PDE’s, 6, (1990), pp. 279–309.

    MATH  Google Scholar 

  9. H.K. DAHLE, R.E. EWING, AND T.F. RUSSELL, Eulerian-Lagrangian localized adjoint methods for a nonlinear convection-diffusion equation. Comp. Meth. Appl. Mech. Engrg. Vol. 122, Nos. 3–4, (1995), 223–250.

    Google Scholar 

  10. C.N. DAWSON, T.F. RUSSELL, AND M.F. WHEELER, Some improved error estimates for the modified method of characteristics, SIAM J. Numer. Anal., 26 (1989), pp. 1487–1752.

    Article  MathSciNet  MATH  Google Scholar 

  11. L. DEMKOWITZ AND J.T. ODEN, An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in two space variables, Comp. Meth. Appl. Mech. Engrg., 55 (1986), pp. 63–87.

    Article  Google Scholar 

  12. L. DEMKOWITZ AND J.T. ODEN, An adaptive characteristic Petrov-Galerkin method for convection-dominated linear and nonlinear parabolic problems in one space variable, J. Comp. Phys. 67 (1986), pp. 188–213.

    Article  Google Scholar 

  13. L. DEMKOWITZ AND J.T. ODEN, An adaptive characteristic Petrov-Galerkin method for convection-dominated linear and nonlinear parabolic problems in one space variable, J. Comp. Phys. 67 (1986), pp. 188–213.

    Google Scholar 

  14. M.S. ESPEDAL AND R.E. EWING, Characteristic Petrov-Galerkin subdomain methods for two-phase immiscible flow, Comp. Meth. Appl. Mech. Engrg., 64 (1987), pp. 113–135.

    Article  MathSciNet  MATH  Google Scholar 

  15. R.E. EWING, ed., Research Frontiers in Applied Mathematics, Vol. 1, SIAM, Philadelphia (1983).

    Google Scholar 

  16. R.E. EWING, Operator splitting and Eulerian-Lagrangian localized adjoint methods for multiphase flow. Whiteman, J. (ed.), The Mathematics of Finite Elements and Applications VII (MAFELAP 1990). Academic Press, Inc., San Diego, (1990), 215–232.

    Google Scholar 

  17. R.E. EWING AND H. WANG, Eulerian-Lagrangian localized adjoint methods for linear advection or advection-reaction equations and their convergence analysis. Computational Mechanics, 12 (1993), 97–121.

    Article  MathSciNet  MATH  Google Scholar 

  18. I. HERRERA, The algebraic theory approach for ordinary differential equations: highly accurate finite differences, Numerical Methods for PDE’s, 3 (1987), pp. 199–218.

    MathSciNet  MATH  Google Scholar 

  19. T.J.R. HUGHES AND A. BROOKS, A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions. Applications to the streamline-upwind procedure (R.H. Gallagher, ed.), Finite Elements in Flu¬ids, 4, Wiley, New York (1982).

    Google Scholar 

  20. C. JOHNSON, Numerical solutions of partial differential equations by the finite element method, Cambridge University Press, Cambridge (1987).

    Google Scholar 

  21. T.F. RUSSELL, Time-stepping along characteristics with incomplete iteration for a

    Google Scholar 

  22. Galerkin approximation of miscible displacement in porous media, SIAM J. Numer. Anal., 22 (1985), pp. 970–1013.

    Google Scholar 

  23. T.F. RUSSELL, Eulerian-Lagrangian localized adjoint methods for advection-dominated problems, Numerical Analysis 1989, Proceedings of the 13th Dundee Conference on Numerical Analysis (D.F. Griffiths and G.A. Watson, eds.), Pitman Research Notes in Mathematics Series, 228, Longman Scientific & Technical, Harlow, U.K. (1989), pp. 206–228.

    Google Scholar 

  24. T.F. RUSSELL AND R.V. TRUJILLO, Eulerian-Lagrangian localized adjoint methods with variable coefficients in multiple dimensions, Computational Methods in Surface Hydrology, Proceedings of the Eighth International Conference on Computational Methods in Water Resources, Venice, Italy (1990), pp. 357–363.

    Google Scholar 

  25. T.F. RUSSELL AND M.F. WHEELER, Finite element and finite difference methods for continuous flows in porous media (R.E. Ewing, ed.), Mathematics of Reservoir Simulation, Frontiers in Applied Math, Philadelphia, Pennsylvania (1983), pp. 35–106.

    Google Scholar 

  26. E. VAROGLU AND W.D.L. FINN, Finite elements incorporating characteristics for one-dimensional diffusion-convection equation, J. Comp. Phys., 34 (1980), pp. 371–389.

    Article  MathSciNet  MATH  Google Scholar 

  27. H. WANG, R.E. EWING, AND T.F. RUSSELL, Eulerian-Lagrangian localized methods for convection-diffusion equations and their convergence analysis. IMA J. Numer. Anal., (submitted).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Scientific Computation, Texas A&M University, College Station, TX, 77843-3404, USA

    Richard E. Ewing

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Hong Wang

Authors
  1. Richard E. Ewing
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Rice University, P.O. Box 1892, Houston, TX, 77843, USA

    Mary Fanett Wheeler

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag New York, Inc.

About this paper

Cite this paper

Ewing, R.E., Wang, H. (1996). Eulerian-Lagrangian Localized Adjoint Methods for Reactive Transport in Groundwater. In: Wheeler, M.F. (eds) Environmental Studies. The IMA Volumes in Mathematics and its Applications, vol 79. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8492-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-8492-2_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8494-6

  • Online ISBN: 978-1-4613-8492-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation