Advertisement

Transport in Porous Media

, Volume 28, Issue 1, pp 51–67 | Cite as

Mathematical Treatment of Point Sources in a Flow Through Porous Media Governed by Darcy's Law

  • Marián SlodičkaEmail author
Article

Abstract

We consider stationary air flow in a porous medium caused by extraction wells and governed by Darcy's law. Point sinks are described by Dirac functions. We distinguish two different situations: locally continuous and discontinuous conductivity near the wells. In both cases, well-posedness is proved. We propose a finite-element scheme in the general case and show the convergence of the approximated solution to the exact one.

point sources Darcy's law jumping conductivity discrete maximum principle gas flow wells 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ciarlet, P. G. and Lions, J. L. (eds), 1991: Finite elements methods (Part I), volume II of Handbook of Numerical Analysis. North-Holland, Amsterdam.Google Scholar
  2. Douglas, J. Jr., Ewing, R.E. and Wheeler, M.F.: 1983, The approximation of the pressure by a mixed method in the simulation of miscible displacement, RAIRO Anal. Numer. 17(1), 17–33.Google Scholar
  3. Ewing, R. E. and Wheeler, M. F.: 1982- 83, Galerkin methods for miscible displacement problems with point sources and sinks - unit mobility ratio case, In Mathematical Methods in Energy Research, Proc. Spec. Year, Univ. Wyoming, 1984, pp. 40–58.Google Scholar
  4. Gilbarg, D. and Trudinger, N. S.: 1983, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, Heidelberg.Google Scholar
  5. Kufner, A., John, O. and Fučik, S.: 1977, Function Spaces, Academia, Prague.Google Scholar
  6. Meyers, N. G.: 1963, An Lp-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Sci. Norm. Sup. Pisa 17, 189–206.Google Scholar
  7. Nieuwenhuizen, R., Zijl, W. and Van Veldhuizen: Flow pattern analysis for a well defined by point sinks. Transport in Porous Media 21, 209–223.Google Scholar
  8. Simader, Ch. G.: 1972. On Dirichlet's Boundary Value Problem, LectureNotes in Math. 268, Springer-Verlag, Berlin, Heidelberg.Google Scholar
  9. Stampacchia, G.: Équations elliptiques du second ordre à coefficients discontinus, Les Presses de Montréal, Montréal.Google Scholar
  10. Wilson, D. J.: Modeling of Insitu Techniques for Treatment of Contaminated Soils: Soil Vapor Extraction, Sparging, and Bioventing. Technomic Publishing, Lancaster, Basel.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of the Federal Armed Forces MunichGermany

Personalised recommendations