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.

Numerical Simulation of 2D Shallow water equation with constant external body force by using Finite difference method

“…Tsunamis are the long waves and eventually occur unlikely other natural VFAST Transactions on Mathematics disaster [7]; these waves are divided into three phases that are, generation, propagation and inundation or up run [6]. Usually, are in series and generated in a body of water that vertically displaced the water by impulsive disturbance [22] .The 2D surface flow is helpful to understand and predict the flow through breach or dyke [14]. These models are also described by the 2D shallow water equation.…”

“…Different types of numerical schemes have been used to find the solution of equations and the results are compared with the experimental results [35,1]. [13], [14]. Numerical simulation of appraisal of climatic conditions for potential solar energy applications are discussed in [13].…”