Author(s): Penghui Hu; Zhixian Cao; Wei Huang; Gareth Pender
Linked Author(s): Wei Huang
Keywords: Well-balanced model; Shallow water flow; Steep slope; Roll waves
Abstract: Traditional numerical models for shallow flows are mostly based on the Saint-Venant equations derived for horizontal or gentle slopes, which however are not generally justified for flows over steep slopes. This paper presents a modified shallow water hydrodynamic model that is generally applicable for flows over arbitrary slopes. It is based on the well-balanced shallow water equations in a topography-linked coordinate system, which fully incorporate the effects of the bottom slope. The governing equations are solved using a second-order accurate Godunov-type finite volume method in conjunction with the HLLC approximate Riemann solver. It is applied to model dam-break flow and roll waves over inclined and fixed beds. In steep-slope cases, the results of the modified model agree with analytical solutions considerably better than the traditional model, although both models produce essentially the same results that match analytical solutions well when the slope is sufficiently gentle. This suggests that the traditional model fails for flows over steep slopes, and thus the application of the modified model is warranted.
Year: 2013