Adding weighted average inter-cell to improve vertical transfer of water

[AquaPore]

Feature type

Changing existing functionality

Improvement Description

Greeting Wflow team,

I propose that implementing a weighted-average inter-cell approach, as used in Richards' equation, to improve the accuracy and speed of computing the unsaturated zone vertical potential transfer of water, Qtransfer due to:

(1) Reduced overshooting of the transfer of water and therefore increased time step without reducing stability;
(2) Improved accuracy by accounting of the amount of water in the cell below;

Currently
$$Qtransfer_{i}^{t}=K\mathrm{sv}_i\left( \frac{\theta _i-\theta _r}{\theta _s-\theta _r} \right) ^{Cbc}$$
were Cbc [-] is the Brooks and Corey exponent, Ksv [L T-1] is the vertical saturated hydraulic conductivity.

Implementation Description

The proposed intercell conductivity using harmonic mean for the Qtransfer:

$$\begin{cases} Qtransfer_{i}^{t}=w_i\left[ K\mathrm{sv}_i\left( \frac{\theta _{i}^{t}-\theta _r}{\theta _s-\theta _r} \right) ^{C_{bc}} \right] +\left[ 1-w_i \right] Qtransfer_{i-1}^{t-1}\\ \omega _i=\frac{\Delta Z_i}{\Delta Z_i+\Delta Z_{i-1}}\\ \end{cases}$$

With kindness,
Joseph A.P. Pollacco

Additional Context

No response