HR: 17:15h
AN: H14B-06    [Abstracts]
TI: An Analytical Form for the Effective Permeability Tensor
AU: * Sviercoski, R
EM: rosangel@math.arizona.edu
AF: Department of Mathematics - University of Arizona, 617 North Santa Rita, Tucson, AZ 85721 United States
AU: Warrick, A
EM: aww@ag.arizona.edu
AF: Soil, Water and Environmental Science - University of Arizona, Shantz Building # 515, Tucson, AZ 85721 United States
AU: Winter, L C
EM: lwinter@ucar.edu
AF: National Center for Atmospheric Research (NCAR), 1850 Table Mesa Drive, Boulder, CO 80305 United States
AB: Upscaling soil hydraulic properties is one of the most challenging problems in Mathematics and Geophysics. Its application runs from Petroleum Engineering, Hydrology and, Soil Science among many others. The idea is to rewrite a partial differential equation describing a physical process in a homogenized or effective form, which takes into account the spatial heterogeneity. We derive an appropriate analytical form, by using the method of homogenization and two-scale asymptotic expansion based on our recently proposed, analytical solution for a sub-problem. Up to now, finding the effective tensor by this method, even though very accurate mathematically, it was very computational demanding. This analytical form provides a huge step towards understanding and modeling multiscale processes. We present numerical simulations for different types of permeability fields including random media and demonstrate that separable and layered media are particular cases.
DE: 3220 Nonlinear dynamics
DE: 3230 Numerical solutions
DE: 1836 Hydrologic budget (1655)
DE: 1866 Soil moisture
DE: 1869 Stochastic processes
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting