Implementation Techniques in Front-Tracking Methods for Moving Boundary Problems with Singularities

  • A. P. Reverberi
  • L. Toro
  • F. Vegliò
Conference paper


Some numerical methods of solution of diffusion problems with moving fronts are considered in this paper. In particular, we pointed out that the accuracy of solution may be endangered when bad matching between initial and boundary conditions are present or un physical oscillations at the moving front are allowed.

We apply a stable and regularised solution method to moving boundary problems with or without particle interaction, and study both the time trend of the front displacement and the values of the dependent variable at the travelling interface.


Implicit Method Implementation Technique Percent Relative Error Move Boundary Problem Front Displacement 


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  1. 1.
    Crank, J. (1984), Free and Moving Boundary Problems, Oxford University Press, Northern IrelandGoogle Scholar
  2. 2.
    Finlayson B.A. (1992), Numerical Methods for Problems with Moving Fronts, Ravenna Park PublishingGoogle Scholar
  3. 3.
    Selim M.S., Seagrave R.C. (1973), Ind. Eng. Chem. Fundamentals, 12: 1CrossRefGoogle Scholar
  4. 4.
    Adrover A., Giona M. (1997), Ind. Eng. Chem. Res., 36: 2452CrossRefGoogle Scholar
  5. 5.
    Furzeland R.M. (1980), J. Inst. Math. Applies., 26: 4111Google Scholar
  6. 6.
    Korn G.A. (1999), Math. Comp. Simulation, 49, 1–2: 129Google Scholar
  7. 7.
    Wilson D.G., Solomon A.D., Boggs P.T. (.Eds.) (1978), Moving Boundary Problems, Academic press, LondonGoogle Scholar
  8. 8.
    Wrobel L.C., Brebbla C.A. (Eds.) (1993), Computational Modelling of Free and Moving Boundary Problems II, Computational Mechanics Publications, Southampton BostonGoogle Scholar
  9. 9.
    Gesmundo F., Castello P., Viani F., Philibert J. (1997), Oxidation of Metals, 47: 1CrossRefGoogle Scholar
  10. 10.
    Gesmundo F., Pereira M. (1997), Oxidation of Metals, 47: 507CrossRefGoogle Scholar
  11. 11.
    Holly K., Danielewski M., Filipek R., Laskawiec J., Milewska A., Zurek Z. (1998), Electrochem. Soe. Proc., 98: 241Google Scholar
  12. 12.
    Danielewski M., Filipek R.. Holly K., Bozek B. (1994), Phys. Stat. Sol.(a) 145: 339CrossRefGoogle Scholar
  13. 13.
    G.D. Smith (1993), Numerical Solutions of Partial Differential Equations, Clarendon Press, OxfordGoogle Scholar
  14. 14.
    Li Z. (1996), Comput. Math. Applies., 31, 3: 9CrossRefGoogle Scholar
  15. 15.
    Li Z., Mayo A. (1994), Proc. Sympos. Appl. Math., 48: 311CrossRefGoogle Scholar
  16. 16.
    Li Z. (1997), Numerical Algorithms, 14: 269CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia, Milan 2002

Authors and Affiliations

  • A. P. Reverberi
    • 1
  • L. Toro
    • 2
  • F. Vegliò
    • 1
  1. 1.DIChePUniversità di GenovaGenovaItaly
  2. 2.Dipartimento di ChimicaUniversità di Roma “La Sapienza”RomaItaly

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