Numerical Simulation of Flooding Using One-dimensional Saint-Venant Equations with Trigonometry Water Level Representation
Maman Yarodji Abdoul Kader, Rabé Badé, Tahirou Aboubacar Haboubacar, Bisso Saley
Current Journal of Applied Science and Technology · pp. 72–79 · Published 28 Feb 2026
10.9734/cjast/2026/v45i24665Abstract
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.
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