Numerical Solutions to Dam Break Wave Propagation

One-dimensional flows in watercourses are modeled by solving Saint-Venant Equations. Understanding these equations and numerical solution of them helps to overcome the problems resulted from propagation of flood and shock waves. In this study, a detailed analysis is implemented to solve one-dimensional dam break problem. Different numerical techniques used for shock capturing are given and their performances are evaluated for two different dam break test cases. Numerical solution is achieved using two different finite-difference schemes; explicit Gabutti and implicit Beam-Warming algorithms, and finite-volume scheme with limiters. Both, finite-difference and finite-volume schemes are second order in time and space. The numerical solutions are compared with analytical results. The errors from the analytical solutions are estimated and presented. The results show that convergence of finite volume schemes is better. The time and spatial variations of water depth and velocity are obtained and will be presented with the animations.