Simulation of 2D Saint-Venant equations in open channel by using MATLAB

Abstract

2D surface flow models are useful to understand and predict the flow through breach, over a dyke or over the floodplains. This paper is aimed at the surface flows to study the behavior of flood waves. The open channel water flow in drains and rivers is considered in view of the fact that such flows are the source of flash flood. In order to predict and simulate the flood behavior, a mathematical model with the initial and boundary conditions is established using 2D Saint-Venant partial differential equations. Next, the corresponding model is discretized by using the explicit finite difference method and implemented on MATLAB. For the testing and implementation purpose a simple rectangular flow channel is considered. The output parameters like height or depth of water z (m), the fluid velocity u (m/s) and the volumetric flow rate Q (m3/sec) are simulated numerically and visualized for the different time steps. The initial simulation results are useful to understand and predict the flood behavior at different locations of flow channel at specific time steps and can be helpful in early flood warning systems. It is also suggested that the coupling of the subsurface flow with the surface flow may provide even better approximations for the flood circulation.