A Finite Volume Shallow Water Hydrodynamic Model and Its Validation

This paper presents a new shallow water hydrodynamic model based on the finite volume MUSCL-Hancock method using a novel fully implicit friction source term discretization. This model has a well-balanced feature and can accurately simulate steady flow in moving water, completely static water flow, and complex flow processes, such as shock wave evolution and energy dissipation in unsteady flow. A total of six typical working conditions were constructed, including well-balanced problems, wet and dry bed (frictionless/friction) dam break, dam-break wave passing through triangular obstacles and cascade dam break. These conditions were validated by combining the analytical solutions of Ritter, Chanson, and others with the measured data. The results indicate that the model demonstrates good agreement with analytical solutions or experimental data in key parameters such as water surface profiles, discharge, and impact pressure evolution, effectively capturing the propagation of dam-break waves. The study confirms that, by coupling the two-dimensional shallow water equations with a high-accuracy numerical scheme, the model exhibits excellent applicability and precision in scenarios involving complex topography and wet-dry moving boundaries. It thus provides a reliable numerical tool for the analysis of complex hydrodynamic processes such as dam-break floods, as well as for disaster assessment, risk forecasting, and mitigation planning.