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Transport in Porous Media

, Volume 69, Issue 2, pp 175–188 | Cite as

A mathematical model of sulphite chemical aggression of limestones with high permeability. Part II: Numerical approximation

  • Giuseppe Alì
  • Vidar Furuholt
  • Roberto Natalini
  • Isabella Torcicollo
Original Paper

Abstract

We present a numerical investigation of a degenerate nonlinear parabolic–elliptic system, which describes the chemical aggression of limestones under the attack of SO2, in high permeability regime. This system has been introduced in the first part of this paper. We present a finite element scheme for our model and its numerical stability is given under suitable CFL conditions. Numerical tests are discussed as well as some examples of the numerical behavior of the solutions.

Keywords

Chemical reactions Porous media Convective and diffusive flows Fast reaction limit Free boundary problems Finite element 

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References

  1. Alì, G., Furuholt, V., Natalini, R., Torcicollo, I.: A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I: modeling and qualitative analysis. Trans Porous Med (2006, this issue)Google Scholar
  2. Aregba-Driollet D., Diele F., Natalini R. (2004) A mathematical model for the SO2 aggression to calcium carbonate stones: numerical approximation and asymptotic analysis. SIAM J. Appl. Math. 64(5): 1636–1667CrossRefGoogle Scholar
  3. Gauri K.L., Bandyopadhyay J.K. (1999) Carbonate Stone: Chemical Behavior, Durability, and Conservation. WileyGoogle Scholar
  4. Guarguaglini, F., Natalini, R.: Large time behavior of solutions to a nonlinear model of sulphation of calcium carbonate stones. IAC Report 52(9/2004); to appear in Communications in PDE; PDF file available at http://www.iac.rm.cnr.it/˜natalini/postscript/guna2004.pdfGoogle Scholar
  5. Varga, R.S.: Matrix Iterative Analysis. Prentice Hall (1962)Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Giuseppe Alì
    • 1
    • 4
  • Vidar Furuholt
    • 2
    • 3
  • Roberto Natalini
    • 2
  • Isabella Torcicollo
    • 1
  1. 1.Istituto per le Applicazioni del Calcolo “M. Picone”, Sez. di NapoliConsiglio Nazionale delle RicercheNapoliItaly
  2. 2.Istituto per le Applicazioni del Calcolo “Mauro Picone”Consiglio Nazionale delle RicercheRomaItaly
  3. 3.SchlumbergerTrondheimNorway
  4. 4.INFN-Gruppo c.CosenzaItaly

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