In this paper, we face the problem of upscaling transmissivity from the
macroscopic to the megascopic scale; here the macroscopic scale is that
of the continuous flow equations, whereas the megascopic scale is that
of the flow models on a coarse grid. In this paper, we introduce the
non-local inverse based scaling (NIBS) and compare it with the
simplified renormalization (SR). The latter is a classical technique
that we adapt to compute internode transmissivities for a finite
differences flow model in a direct way. NIBS is implemented in three
steps: in the first step, the macroscopic transmissivity, together with
arbitrarily chosen auxiliary boundary conditions and sources, is used
to solve forward problems (FPs) at the macroscopic scale; in the second
step, the resulting heads are sampled at the megascopic scale; in the
third step, the upscaled internode transmissivities are obtained by
solving an inverse problem with the differential system method (DS) for
which the heads resulting from the second step are used. NIBS is a
non-local technique, because the computation of the internode
transmissivities relies upon the whole transmissivity field at the
macroscopic scale. We test NIBS against SR in the case of synthetic,
isotropic, confined aquifers under the assumptions of two-dimensional
(2D) and steady-state flow; the aquifers differ for the degree of
heterogeneity, which is represented by a normally distributed
uncorrelated component of In T. For the comparison, the reference heads
and fluxes at the megascopic scale are computed from the solution of
FPs at the macroscopic scale. These reference values are compared with
the heads and the fluxes predicted from models at the megascopic scale
using the upscaled parameters of SR and NIBS. For the class of aquifers
considered in this paper, the results of SR are better than those of
NIBS, which hints that non-local effects can be disregarded at the
megascopic scale. The two techniques provide comparable results when
the heterogeneity increases, when the megascopic scale is large with
respect to the heterogeneity length scale, or when the source terms are
relevant. (C) 2001 Elsevier Science Ltd. All rights reserved.