Application of Finite Difference Schemes to 1D St. Venant for Simulating Weir Overflow

Abstract

Depth averaged equations are commonly used for modelling hydraulics problems. Nevertheless, the model may not be able to accurately assess the flow in the case of different flow regimes, such as hydraulic jump. The model requires appropriate numerical method or other numerical treatments in order to simulate the case accurately. A finite volume scheme with shock capturing may provide a good result, but it is time consuming as compared to the commonly used finite difference schemes. In this study, 1D St. Venant equation is solved using Artificial Viscosity Lax-Wendroff and Mac-Cormack with TVD filter schemes to simulate an experiment case of weir overflow. The case is chosen to test each scheme ability in simulating flow under different flow regimes. The simulation results are benchmarked to the observed experimental data from previous study. Additionally, to observe the scheme efficiency, the simulation time between the models are compared. Therefore, the most accurate and efficient scheme can be determined.