Some practical aspects of numerical methods for parabolic equations

Flow through heterogeneous porous media is well represented by
parabolic equations. One of the well known practical aspects of this
theory is groundwater movement through soil.

The talk  is dedicated to the problem of large scale groundwater
modeling where the available groundwater level data and pumping tests
are scarce, and in addition, the spatial distribution of the
groundwater data is not homogeneous. For a specific pumping area, head
data are available, while for other large areas of the aquifer limited
data is available. In such an aquifer the use of the classical
numerical methods may lead to inaccurate results. This is due to the
fact that the whole calibration process is validated using limited and
scarce groundwater data. Thus, in regions where head data are not
available the calibration is less accurate. Moreover, the head results
are sensitive to changes of the permeability parameters.

In the present contribution, we propose a modeling approach based on
cell model. The present cell model (called the ACM method) is
currently operating at a regional scale and its goal is to compute the
groundwater fluxes entering into or leaving a given region using a
first level calibration model that conserves the mass balance. The
cell model is derived from the general groundwater flow equations
using a finite volume approach combined with a mixed formulation.
Within this advanced cell model, the cells are defined according to
the hydrogeology of the aquifer and the state variables may be whether
the water level and/or the flux rate entering or leaving the cells.
The general software was developed using MATLAB 7 software connected
via COM technology with a Visual Basic graphical user interface.

The approach was implemented on a real case study of the Yarkon
Taninim aquifer in Israel

The ACM approach allows introducing to the model recharge input and
boundary conditions at a large scale. This enables getting better
estimates of the mass balance in the aquifer.

Also the ACM model may be used as a pre-model for large scale modeling
and combined with a high resolution model for a specific region where
the boundary conditions are created by the ACM model.