Determination of the free surface in a 2D horizontal model is equivalent to the computation of the unknown thickness. The computed thickness (m) of an unconfined aquifer must be such that it ensures that the resulting potential head (h) fulfils the equation

 

 

in which u represents the lower boundary of the aquifer. The iteration of the thickness is carried out for each single element. In each step, the thickness is determined with:

 

with: i = iteration step

To avoid oscillations, the change of the thickness for the next step of iteration is multiplied by an attenuation factor 0 < w < 1:

 

 

For w=1.0, the iteration is not attenuated at all; for w=0, the attenuation is maximal. The default value is 0.5. The computed thickness values from the model checking are used as initial thickness for the iteration.

The iteration process is continued until the difference between the two computed potential heads is less than an internal limit, or until the user-defined maximum number of iteration steps is reached.

For the case of a confined aquifer, the groundwater surface cannot move upwards. The iteration takes this into account, and the computed thickness is not allowed to be larger than the maximum (possible) thickness computed in the model checking.

The definition of the lower boundary of the aquifer (UNTE) is absolutely necessary in order to carry out an iteration of the thickness in a 2D model.

 

Example:

For instance, a calibrated state is to be verified where the model file contains initial potential heads (EICH) and the lower boundary of the aquifer (UNTE). Hence it follows that the initial thickness is actually very close the thickness to be found. Therefore, an iteration using an attenuation factor w=1.0 will converge rapidly and approach the final thickness.

Generally, further calculations consider a new groundwater situation, e. g. changing exfiltration rates. Hence the iterated thickness in the corresponding area will be different from the initial thickness. Rapidly changing boundary conditions or a "bad" initial thickness makes the attenuation necessary in order to avoid possible oscillations.

 

Special feature of the module SITRA:

In the module SITRA the thicknesses are stored as node values. Therefore the initial and maximum thicknesses computed in the model checking have to be averaged on node values, which may eventually lead to a loss of accuracy.

 

Calculation of the free surface (vertical- or 3D model)