Non-hydrostatic numerical modeling of hydraulic jump over a weir

Abstract

Weir is the construction widely used in hydraulic engineering. It is very important to investigate the behaviors of the flows over a weir. In general when water streams over a weir it behaves various flow patterns according to different flow conditions. Different flow patterns results in different inference on the water level profile and the distribution of recirculation zones at downstream of the weir. The simulation of these flows is of general practical interest to the design of hydraulic structures and the management of water resources. In this report, a view of how to simulation hydraulic jump over a weir is presented, from 1-D model, 2DV hydrostatic model, 2DV non-hydrostatic model using pressure gradients as unknowns, 2DV non-hydrostatic model using pressures as unknowns, to 2DV implicit non-hydrostatic model. A 2DV implicit non-hydrostatic numerical scheme is presented, which can simulate flows with steep water and bed level gradients. The numerical algorithm solve the Reynolds equations and The integrated continuity equation simultaneously, so that the water surface level is integrated into the system, and solved together with the pressure fields. The resulting algorithm is locally and globally mass conservative. Several numerical experiments illustrate the potential of the model, namely: the simulation of the water level and velocity fields of free, undular and submerged hydraulic jumps downstream of a weir. This model is proved to fairly accurately represent discontinuities in bottom topography and water surface profiles. The numerical model also has the ability to describe different flow regimes downstream of a weir, namely free flow, undulation, and fully submerged flow. The results from the numerical model show a fair agreement with the experimental data. The implicit non-hydrostatic model, provides correct wave heights, wave lengths, and predicts the upper and lower limit for the occurrence of undulations in a good manner.