Numerical Simulation of Flooding Using One-dimensional Saint-Venant Equations with Trigonometry Water Level Representation
Maman Yarodji Abdoul Kader *
Department of Discipline Didactics, Faculty of Education Sciences, Djibo Hamani University, Tahoua, Niger.
Rabé Badé
Department of Mathematics and Computer, Faculty of Science and Technology, Abdou Moumouni University, Niamey, Niger.
Tahirou Aboubacar Haboubacar
Department of Mathematics and Computer, Faculty of Science and Technology, Abdou Moumouni University, Niamey, Niger.
Bisso Saley
Department of Mathematics and Computer, Faculty of Science and Technology, Abdou Moumouni University, Niamey, Niger.
*Author to whom correspondence should be addressed.
Abstract
This paper presents a numerical study of flooding using the one-dimensional Saint-Venant (shallow water) equations, which describe the conservation of mass and momentum in free-surface flows. The model is developed under simplified assumptions, including flat topography and the absence of additional source terms such as friction or rainfall.
Sinusoidal functions are used to define the initial water level profile and analyze spatial flow variations. The numerical solution is obtained using the finite volume method with β - Rusanov and HLL flux schemes, and wall-type boundary conditions are applied at the domain edges. The results illustrate the evolution toward hydraulic equilibrium, with increasing water height and decreasing velocity demonstrating the qualitative effectiveness of the proposed approach for understanding flood dynamics in a controlled setting.
Keywords: Flooding, Saint-Venant equation, trigonometry, finite volume method, numerical simulation