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An ELLAM Scheme for Porous Medium Flows

  • Hong Wang
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)

Abstract

An Eulerian-Lagrangian localized adjoint method (ELLAM) is presented for coupled systems of fluid flow processes occurring in porous media with point sources and sinks. The ELLAM scheme symmetrizes the governing transport equation, greatly eliminates non-physical oscillation and/or excessive numerical dispersion present in many large-scale simulators widely used in industrial applications. It can treat large mobility ratios, discontinuous permeabilities and porosities, anisotropic dispersion in tensor form, and point sources and sinks. It also conserves mass. Numerical experiments are presented. The relationship between ELLAM and discontinuous Galerkin methods (DGMs), and the possibility of developing a hybrid ELLAM-DGM scheme are discussed.

Keywords

Trial Function Discontinuous Galerkin Method Reservoir Simulation Mobility Ratio Local Truncation Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bear, J.: Hydraulics of Groundwater. McGraw-Hill, New York, 1979Google Scholar
  2. 2.
    Celia, M.A., Russell, T.F., Herrera, I., Ewing R.E.: An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation. Adv. Wat. Res. 13 (1990) 187–206CrossRefGoogle Scholar
  3. 3.
    Chavent, G, Cockburn, B.: The local projection P 1-discontinuous Galerkin finite element method for scalar conservation laws. M2AN 23 (1989) 565–592MathSciNetzbMATHGoogle Scholar
  4. 4.
    Chen, Z., Cockburn, B., Jerome, J.W., Shu C.W.: Mixed-RKDG finite element methods for the 2-D hydrodynamic model for semiconductor device simulation. VLSI Designs 3 (1995) 1–14CrossRefGoogle Scholar
  5. 5.
    Cockburn, B., Shu C.W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: general framework. Math. Comp. 52 (1989) 411–435MathSciNetzbMATHGoogle Scholar
  6. 6.
    Ewing, R.E. (ed.): The Mathematics of Reservoir Simulation, Research Frontiers in Applied Mathematics. 1, SIAM, Philadelphia, 1984Google Scholar
  7. 7.
    Ewing, R.E., Russell, T.F., Wheeler, M.F.: Simulation of miscible displacement using mixed methods and a modified method of characteristics. SPE 12241 (1983) 71–81Google Scholar
  8. 8.
    Falk, R., Richter, G.R.: Local error estimates for a finite element method for hyperbolic and convection-diffusion equations. SIAM J. Numer. Anal. 29 (1992) 730–754MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    LeSaint, P., Raviart, P.A.: On a finite element method for solving the neutron transport equation. DeBoor, C. (ed.), Mathematics Aspects of Finite Elements in Partial Differential Equations, Academic Press, (1974) 89–123Google Scholar
  10. 10.
    Morton, K.W., Priestley. A., Süli, E.: Stability of the Lagrangian-Galerkin method with nonexact integration. RAIRO M2AN 22 (1988) 123–151Google Scholar
  11. 11.
    Peaceman, D.W.: Fundamentals of Numerical Reservoir Simulation. Elsevier, Amsterdam, 1977Google Scholar
  12. 12.
    Reed, W.H., Hill, T.R.: Triangular mesh methods for the neutron transport equation. Los Alamos Scientific Laboratory Report LA-UR-73–479, 1973Google Scholar
  13. 13.
    Wang, H.: A family of ELLAM schemes for advection-diffusion-reaction equations and their convergence analyses. Numer. Meth. PDEs 14 (1998) 739–780zbMATHGoogle Scholar
  14. 14.
    Wang, H., Dahle, H.K., Ewing, R.E., Espedal, M.S., Sharpley, R.C., Man, S.: An Eulerian-Lagrangian localized adjoint method for advection-dispersion equations in two dimensions and its comparison to other schemes. SIAM J. Sci. Comp. (in press)Google Scholar
  15. 15.
    Wang, H., Ewing, R.E., Qin, G., Lyons, S.L., Al-Lawatia, M, Man, S: A family of Eulerian-Lagrangian localized adjoint methods for multi-dimensional advection-reaction equations. J. Comp. Phys. 152 (1999) 120–163MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hong Wang
    • 1
  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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