# Supercritical discharge modelling

However, the problem won’t be solved in unsteady flow, since some sections will be in critical flow, which generate numeric instabilities and stop the calculations because of passages in supercritical flow. A better solution for guaranteeing a calculation in steady flow and also in unsteady flow is to define a weir at every important fall, passing by critical depth Yc (curve F2). In this case, the upstream depth of the fall will be calculated by this weir equation, and won’t be Yc. Hydraulically, we do not calculate the depth immediately upstream from the fall (Yc), but slightly upstream from this fall, in a zone where the water trickle contraction is negligible and where the hypothesis of hydrostatic distribution of pressures holds true (Cf. usual demonstrations of weir equations).

The problem that remains is to define the parameters of this weir. Normally, it would be necessary to give the real geometry of the section. However this is not possible (except in the simple case of a rectangular section), since only the horizontal weirs can be modelled in SIC. However, if the section is almost a rectangular section, a horizontal weir were frame level is equal to the bottom level, is a good approximation. Otherwise, the use of several weirs in parallel as indicated in the previous chapter that deals with the triangular weirs permits you to model weirs of a more complex shape. In any case, it will also be necessary to provide a discharge coefficient for the weir, that can arbitrarily be equal to 0.4 or calibrated by measures on the ground.

The same problem can also occur at abrupt geometry changes (widening), with local passage to Yc. The solution to use is the same. when these corrections have been done, the calculated flow profile is more realistic.

In spite of these corrections that permit you to better model existing falls at some point in the system there still may remain many points where the discharge is supercritical (Cf. the .BAK file).

Often these passages in supercritical take place far from the offtakes. This is relatively normal because in general a gravity offtake is placed in a fluvial discharge zone, in order to control its feed level. We can thus imagine simplifying the supercritical zone model by using abrupt falls equipped with weirs. when these modifications have been done, we get an entirely fluvial flow profile (Cf. .BAK file).
The passage problem at the critical depth Yc or the passage problem in supercritical discharge can be solved by doing a modification in the geometry of the system. It will be necessary during the calibration of the model, not to pay attention to zones where these modifications have taken place, but to be vigilant elsewhere, and to check that these geometry modifications don’t change the results in fluvial discharge zones too much.