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

Abstract

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.

Enhanced physics‐informed neural networks for efficient modelling of hydrodynamics in river networks

“…Various numerical techniques exist for discretizing SVE, with finite difference schemes (El Kadi Abderrezzak & Paquier, 2009; Sen & Garg, 2002) often preferred for their computational efficiency and ease of implementation. The finite volume method has also seen application, primarily in 2D scenarios (Hodges, 2019; Kesserwani, Ghostine, Vazquez, Ghenaim, & Mosé, 2008; Sarkhosh et al, 2020). While iterative techniques like the Newton–Raphson method (Janicke & Kost, 1998; Zhu et al, 2011) are generally used to solve the resulting non‐linear algebraic equations, the direct solution becomes computationally challenging and storage‐intensive in the case of multi‐channel networks due to the complicating factor of junctions.…”

Random-walk-path solution of unsteady flow equations for general channel networks

“…Finite difference schemes (El Kadi Abderrezzak and Paquier, 2009;Qi et al, 2022;Sen and Garg, 2002) are the most commonly applied techniques due to their advantages, such as a small amount of computation and ease of implementation. In the past two decades, the finite volume method (Hodges, 2019;Kesserwani et al, 2008a;Sarkhosh et al, 2020) was widely applied to solve the Saint-Venant equations, limited mostly to 2D cases (Liang et al, 2007;Zhao et al, 2019). The non-linear equations are solved using iterative techniques such as the Newton-Raphson method (Janicke and Kost, 1998;Zhu et al, 2011) or through linearization.…”