A kinetic interpretation of the section‐averaged Saint‐Venant system for natural river hydraulics

Abstract

SUMMARYThe classical Saint-Venant system is well suited for the modeling of dam breaks, hydraulic jumps, reservoir emptying, flooding etc. For many applications, the extension of the Saint-Venant system to the case of non-rectangular channels is necessary and this section-averaged Saint-Venant system exhibits additional source terms. The main difficulty of these equations consists of the discretization of these source terms.In this paper we propose a kinetic interpretation for the section averaged Saint-Venant system and derive an associated numerical scheme. The numerical scheme-2nd order in space and time-preserves the positivity of the water height, and is well-balanced. Numerical results including comparisons with analytic and experimental test problems illustrate the accuracy and the robustness of the numerical algorithm.

SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies

“…More precisely, these equations model a flow in a rectilinear three-dimensional channel with the quantities averaged not only on the vertical direction but also on the width of the channel. For the derivation, see for example [26]. Remark 1, mentioned for Mac Donald's type 1D solutions, applies to these pseudo-2D solutions too.…”

On the modeling and simulation of non-hydrostatic dam break flows

“…Simulation results of the water depth are in agreement with the experimental data for all the four markers. Actually, results at the third marker S 3 are significantly better than those given, e.g., in [19] when using an hydrostatic simplified model. On the other hand, results at the fourth marker S 4 are less accurate due to the very shallow behavior of the water after the constriction (meaning shallow water-like models are more adapted here).…”

“…The channel has a constriction approximately 12 [m] away from the left extremity of the domain. The experimental conditions, as well as the geometrical quantities, are fully described in [19,20] and illustrated in Figure 10 finite element mesh in Figure 11. It is thus a good benchmark to validate the use of 3D simulations and compare with simplified models or experimental data.…”

“…Measured values of the water level are available at four given points, labeled S 1 through S 4 , and illustrated in Figure 10. Figure 12 visualizes a comparison of the time evolution of the water level at these four markers with experimental data [19,20]. The approximation of the water height is computed on the grid of small cells.…”

A coupled atmospheric–hydrologic modeling system with variable grid sizes for rainfall–runoff simulation in semi-humid and semi-arid watersheds: how does the coupling scale affects the results?

“…The WRF rainfall simulation is sensitive to the selection and the combination of its physical parameterizations (Di et al, 2015). In this study, the well-performing and extensively used parameterizations in northern China were chosen (Miao et al, 2011;Di et al, 2015;Tian et al, 2017a), which include two microphysics parameterizations, i.e., Purdue-Lin (Lin) (Lin et al, 1983) and WRF Single-Moment 6 (WSM6) (Hong et al, 2006); two cumulus parameterizations, i.e., Kain-Fritsch (KF) (Kain, 2004) and Grell-Devenyi (GD) (Grell and Freitas, 2014); and two PBL (planetary boundary layer) parameterizations, i.e., Mellor-Yamada-Janjic (MYJ) (Hong et al, 2006) and Yonsei University (YSU) (Janjić, 1994). Besides, Rapid Radiative Transfer Model (RRTM) and Dudhia (Evans et al, 2012) usually cooperate well as the long-and shortwave radiation parameterizations, and Noah is chosen to be the land surface model (Chen et al, 2014).…”