

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 doubleporosity soils by the method of homogenization Doubleporosity soils are characterized by the presence of two regions with
very different hydraulic properties. One region is associated with highly
permeable intraaggregate pores, macropores or fissures, the other region
consists of weakly permeable aggregates or porous blocks. This particular
structure gives rise to nonequilibrium phenomena during flow and transport
processes. These effects cannot be captured by standard singleporosity models
and special approaches are required.
The presentation focuses on the development of macroscopic models of flow in
doubleporosity 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 nonequilibrium 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:
 Auriault, J.L. (1991), Heterogeneous medium: Is an equivalent macroscopic
description possible?, Int. J. Engng Sci., 29(7), 785795.
 Gerke H. H., and M. Th. van Genuchten (1993) A dualporosity model for
simulating the preferential movement of water and solutes in structured porous
media, Water Resour. Res., 29(2), 305319.
 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.
 SanchezPalencia, E. (1980) Nonhomogeneous media and vibration theory, Lecture
Note in Physics, vol. 127, SpringerVerlag, Berlin.
 

