WIT Press

Application Of Integrated Finite Differences To Compute Symmetrical Upscaled Equivalent Conductivity Tensor


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C. Vassena & M. Giudici


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:


upscaling, equivalent conductivity, symmetry, integrated finitedifferences.