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Institut für Wasserbau - IWS

Selected Topics and International Network Lectures

Druckansicht
 
Donnerstag
06.05.2004
16:00 Uhr
Adam Szymkiewicz, Laboratoire LTHE, Université Joseph Fourier, Grenoble, France / Gdansk University of Technology, Gdansk, Poland

Modeling of water flow in double-porosity soils by the method of homogenization

Double-porosity soils are characterized by the presence of two regions with very different hydraulic properties. One region is associated with highly permeable intra-aggregate pores, macropores or fissures, the other region consists of weakly permeable aggregates or porous blocks. This particular structure gives rise to non-equilibrium phenomena during flow and transport processes. These effects cannot be captured by standard single-porosity models and special approaches are required.
The presentation focuses on the development of macroscopic models of flow in double-porosity soils by the method of asymptotic homogenization. This method allows to derive the macroscopic models from the description of physical processes at the local scale, without any a priori assumptions on the final form of the model. The domain of validity of the model is precisely defined by the analysis of dimensionless numbers governing the flow. The effective macroscopic conductivity of the medium is defined as the function of local conductivity and geometry of the medium. For the non-equilibrium flow one obtains a single macroscopic equation with integral source term describing the water transfer between two regions.
Several numerical examples are presented. The results obtained by homogenization are compared to the phenomenological model of Gerke and van Genuchten and to the fine scale reference solution, where the heterogeneous structure of the medium is explicitly represented. The simulations show that the model obtained by homogenization gives results close to the reference solution and correctly estimates the effective parameters.

References:

  1. Auriault, J.-L. (1991), Heterogeneous medium: Is an equivalent macroscopic description possible?, Int. J. Engng Sci., 29(7), 785-795.
  2. Gerke H. H., and M. Th. van Genuchten (1993) A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media, Water Resour. Res., 29(2), 305-319.
  3. Lewandowska, J., A. Szymkiewicz, K. Burzy?ski, and M. Vauclin (2004) Modeling of unsaturated water flow in double porosity soils by the homogenization approach, Advances in Water Resources, in press.
  4. Sanchez-Palencia, E. (1980) Non-homogeneous media and vibration theory, Lecture Note in Physics, vol. 127, Springer-Verlag, Berlin.