Analytical and numerical modeling of shallow water flow in a channel: Theoretical approaches and simulations

This study focuses on the modeling and simulation of shallow water flows in a channel through the application of the Saint-Venant equations. Two main approaches were explored: an analytical solution and a numerical method based on finite difference discretization. The analytical solution provides exact expressions for water depth and velocity under simplified conditions, offering a reference point for validating numerical simulations. The numerical method, on the other hand, captures more complex dynamics such as wave propagation and nonlinear interactions between sections of the channel. The simulations reveal an inverse relationship between water depth and flow velocity, confirming the validity of the governing equations. Moreover, the influence of parameters such as channel slope, flow rate, and boundary conditions on the system?s dynamics is clearly illustrated. The comparative analysis of the two approaches shows that the finite difference method is a powerful tool for practical applications in hydraulic engineering, allowing for the accurate modeling of real-world phenomena while offering greater flexibility compared to idealized analytical solutions.