A one-dimensional semi-implicit finite volume modeling of non-inertia wave through rockfill dams

For hydraulic routing through coarse rockfill dams, there is still debate on whether the inertia terms might be neglected as a result of the drag force generated by the rock materials. In this study, a one-dimensional unsteady model for flow-through rockfill dams is built. For this purpose, inertia terms of Saint-Venant equations are disregarded. A semi-implicit scheme adopted for linearizing the nonlinear friction term within the time integration satisfies the Courant-Friedrich-Lewy stability criterion. The most challenging issue in the modeling of flows through rockfill dams is the appropriate definition of boundary conditions at the dam's exit zone. In addition to the analysis of different exit boundary conditions proposed in the literature, a Neumann-type boundary condition suitable for the non-inertia wave equation is also employed to estimate the exit boundary condition. This procedure is basically in appreciation of the nonlinear behavior of the water surface closer to the exit boundary. Due to the existence of the sloping edges in the trapezoidal-shaped dam, an effective length is considered for the solution domain. Finally, the model is compared with observed data and a dynamic wave model. A very good match is observed, which builds confidence in the presented modeling approach.