Application of integrated finite differences to compute symmetrical upscaled equivalent conductivity tensor

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. Previous works 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.