Analysis of Transport Processes for Layered Porous Materials Used in Industrial Applications

  • H. Neunzert
  • A. Zemitis
  • K. Velten
  • O. Iliev


This work was aimed at the development of mathematical models and corresponding numerical solution and parameter estimation procedures which are needed as a basis for the computer-aided design of layered porous materials for industrial applications (e.g., hygienic products, technical textiles). The applications lead to nonlinear partial differential equations which must be solved in complex 3D geometries in many cases. Additionally, they may involve saturated/unsaturated flow, coupled flow and deformation problems, swelling particles, large jumps of the material parameters at the interfaces, convection dominance and complex boundary conditions. We introduce a generic mathematical model for layered porous materials, discuss some of the numerical aspects with an emphasis on 3D geometry description and present example applications.


Porosity Convection Exter 


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  1. 1.
    J. Bear and Y. Bachmat, Introduction to modelling of transport phenomena in porous media, Series in mechanical engineering (Kluwer Academic publishers, 1990).Google Scholar
  2. 2.
    Mechanics of poroelastic media, Solid mechanics and its applications, v. 41, S. A.P.S., ed., (Kluwer, 1995).Google Scholar
  3. 3.
    J. Bear and A. Verruijt, Modelling groundwater flow and pollution (Reidel, Dordrecht, 1987).CrossRefGoogle Scholar
  4. 4.
    A. A. Samarskij, Theorie der Differenzenverfahren, Mathematik und ihre Anwendungen in Physik und Technik; Bd. 40 (Leipzig: Geest u. Portig, 1984).Google Scholar
  5. 5.
    R. Ciegis and A. Zemitis, “Numerical algorithms for simulation of the liquid transport in multilayered fleece”, In 15th IMACS World Congress on Scientific Computation and Applied Mathematics, pp. 117–122 (Wissenschaft und Technik Verlag Berlin, 1997).Google Scholar
  6. 6.
    D. Adalsteinsson and J. A. Sethian, “A fast Level Set method for propagating interfaces”, Journal of computational Physics 118, 269–277 (1994).MathSciNetCrossRefGoogle Scholar
  7. 7.
    M. Sussman, P. Smereka, and S. Osher, “A Level Set Aproch for Computing Solutions to Incompressible Two-Phase Flow”, Journal of computational Physics 114, 146–159 (1994).MATHCrossRefGoogle Scholar
  8. 8.
    J. A. Sethian, Level Set Methods (Cambridge University Press, 1996).Google Scholar
  9. 9.
    R. K. M. Moog and A. Zemitis, “Some numerical aspects of the level set method”, In Mathematical modelling and analysis, vol. 3 pp. 140–151 (Vilnius “Technika”, 1997).MathSciNetGoogle Scholar
  10. 10.
    A. A. Samarskij and P. N. Vabishchevich, Computational heat transfer, Volume 1, Mathematical Modelling (John Wiley & Sons, 1995).Google Scholar
  11. 11.
    T. I. T. R. Glowinski T. W. Pan and D. D. Joseph, “A distributed Lagrange multiplier/fictitious domain method for particulate flows”, Int. J. Multiphase Flow 25, 755–794 (1999).MATHCrossRefGoogle Scholar
  12. 12.
    J. Weickert, “A mathematical model for diffusion and exange phenomena in ultra napkins”, Math. Meth. Appl. Sci. 16, 759–777 (1993).MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Modern superabsorbent polymer technology, B. L. and G. A.T., eds., (Wiley-VCH, 1998).Google Scholar
  14. 14.
    O. H., H. S.A., S. P.G., and M. L, “A model for the swelling of superabsorbent polymers”, Polymer 39, 6697–6704 (1998).Google Scholar
  15. 15.
    X. D. L. R. P. Fedkiw and M. Kang, uCLA CAM Report (unpublished).Google Scholar
  16. 16.
    R. L. R. Ewing and O. Iliev, “A modified finite volume approximation of second order elliptic equations with discontinuous coefficients”, Technical Report No. ISC-99-01-MATH, Texas University (1999).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • H. Neunzert
    • 1
  • A. Zemitis
    • 1
  • K. Velten
    • 1
  • O. Iliev
    • 1
  1. 1.Institute of Industrial MathematicsKaiserslauternGermany

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