Application Of Integrated Finite Differences To
Compute Symmetrical Upscaled Equivalent
Conductivity Tensor
Author(s)
C. Vassena & M. Giudici
Abstract
The equivalent conductivity tensor is computed with a method based on the
solution of the balance equation at the fine scale. In particular the balance equation
is solved on a block assigning Dirichlet boundary conditions that vary linearly with
the space coordinates and the equivalent conductivity tensor is the linear tensor
relating average flux and hydraulic gradient. Previousworks prove that this method
yields a symmetric equivalent conductivity tensor both for continuous domains
and for discrete models based on integrated finite differences. Here the equivalent
conductivity tensor is computed for two lateral faces of a volume of glacio-fluvial
sediments and the results are compared with those obtained with a standard finite
differences method on square grids with different spacings.
Keywords: upscaling, equivalent conductivity, symmetry, integrated finite
differences.
1 Introduction
Discrete models of ground water flow are usually based on the discretisation
of the subsurface in grid-blocks for which homogeneous equivalent blockscale
hydraulic conductivities must be specified. In real porous media the
local scale K tensor is heterogeneous within a block and therefore it is
necessary to find an equivalent conductivity tensor, K, for each grid-block.
The basic idea for upscaling is that the block-averaged Darcy’s velocity,
q, and hydraulic gradient, J, are related by a block-scale Darcy’s law:
Keywords
upscaling, equivalent conductivity, symmetry, integrated finitedifferences.
Related Book
Other papers in this volume
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