Numerical study using an implicit finite difference scheme of a high velocity flow crossing a non-prismatic hydraulic structure - case of symmetrical gradual expansion

The objective of the present research work is the numerical simulation of a supercritical flow through a non-prismatic channel. The unsteady flow is governed by the 2D Saint Venant equations. These equations are discretised using the Beam and Warming implicit finite difference scheme. The elaborated numerical model is tested in the case of a symmetrical gradual expansion. First, the aim is to determine the shape of the water surface along the solid wall and the median axis for a weak bottom slope. Subsequently, the study is generalised for steeply sloping channels. The obtained results in the first application show that there are no significant disturbances in the water surface, which did not lead to the appearance of the rather dangerous transverse waves. In the second one, it was observed that by increasing the bottom slope the flow does not extend laterally towards the walls because their divergence is very gradual.