With this approach, the unsaturated areas of the aquifer are fully included in the FE calculation. The flow equation is considered in its form as a pressure equation. A degree of saturation Sr = Sr(p) is calculated from the current pressure p for each mesh node. A relative K value kr = kr(Sr) is then calculated for each element from the saturation values of all corner nodes:

pressure p_i Saturation S_{r, i+1} and relative K-value k_{r, i+1}

with: i = iteration step

To avoid oscillations during iteration, the change in the relative K values from one iteration step to the next is given an attenuation factor of 0< w < 1:

k_{r, i+1} = k_{r, i}) + w * (k_{r, i+1} - k_{r, i})

with: i = iteration step

At w=1.0 the iteration is not attenuated at all, at w=0. it is extremely attenuated/damped. The default setting is usually an attenuation factor of w=0.5. The initial state for the iteration is taken from the calibration potential heads, or from the potential heads of the null file, or relative K values specially calculated using the ASAT attribute (initial saturation). Otherwise, the relative K values are set to the initial value of 1.0.

Within an iteration step, the relative k value is adjusted until the differences in the calculated potential heads of two steps fall below the iteration threshold entered by the user.

Remark:

When iterating the free surface, numerical problems can occur with poorly-chosen model parameters, which in the worst case can lead to the iteration not converging.

The main cause for this is high areal recharge rates for unsaturated regions. The iteration methods then tends to oscillate:

If the elements are 'open' (k = 1 or kr = 1), the free surface falls below the position height of the elements. This means that the elements become unsaturated in the next iteration step, i.e. 'impermeable' (k 0 or kr 0). Due to the high inflow rates, a 'potential head mound' forms on these impermeable elements and the elements are saturated again in the next iteration step, i.e. 'open'.

In many cases, these oscillations can be avoided by a strong attenuation coefficient, which, however, also slows down the convergence speed and thus requires a larger number of iterations.

Input parameters