Analysis of Transport Processes for Layered Porous Materials Used in Industrial Applications
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.
KeywordsPorosity Convection Exter
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- 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.Mechanics of poroelastic media, Solid mechanics and its applications, v. 41, S. A.P.S., ed., (Kluwer, 1995).Google Scholar
- 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.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
- 8.J. A. Sethian, Level Set Methods (Cambridge University Press, 1996).Google Scholar
- 10.A. A. Samarskij and P. N. Vabishchevich, Computational heat transfer, Volume 1, Mathematical Modelling (John Wiley & Sons, 1995).Google Scholar
- 13.Modern superabsorbent polymer technology, B. L. and G. A.T., eds., (Wiley-VCH, 1998).Google Scholar
- 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- 15.X. D. L. R. P. Fedkiw and M. Kang, uCLA CAM Report (unpublished).Google Scholar
- 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