The formulation of internal boundary conditions in unsteady 2‐D shallow water flows: Application to flood regulation

Abstract

[1] This work presents a two-dimensional hydraulic model that includes gates as internal structures. The flow is modeled using the two-dimensional shallow water equations and the gates are formulated as internal boundary conditions to provide a simulation tool for water flood management. When open channel flow in a river passes through a gate, the shallow water equations are no longer valid and energy conservation laws are required. The change in the set of equations is avoided by modeling gates as a spatial discontinuity or internal boundary condition, providing an alternative algorithm to the one used in the rest of the flooded computational domain. In the first part of this work, the requirements of an adequate discretization for gate modeling are provided in the context of a finite volume numerical scheme able to handle all kind of flow regimes over complex bed topography. In the second part of this work, the formulation of the internal boundary conditions is verified by means of a test case with exact solution. A benchmark test case is then proposed as a synthetic river reach with lateral storage areas controlled by gates. Dimensional analysis is used to establish the regulation parameters influencing the attenuation of the outlet peak discharge. It is also shown that the peak outflow discharge can be reduced by coupling the present simulator with a proportional-integral-derivative regulation algorithm. Finally, a river reach of the Ebro River is simulated with a real flooding scenario.Citation: Morales-Hernandez M., J. Murillo, and P. Garcıa-Navarro (2013), The formulation of internal boundary conditions in unsteady 2-D shallow water flows: application to flood regulation, Water Resour. Res., 49,

Two-Dimensional Numerical Simulation of Bed-Load Transport of a Finite-Depth Sediment Layer: Applications to Channel Flushing

“…It is only in the DR, where actual vertical walls occur, that the wetted perimeter can be somewhat poorly represented. Flushing in the tank is controlled by a fast-opening gate between the upstream and middle reaches, with dimensions of 6 × 1 m, and is assumed to go from closed to fully open at a constant rate in 5 or 10 s. The numerical representation of the time-dependent gate opening is described by Morales-Hernández et al (2013). The domain is closed in all boundaries except the downstream boundary, where the tunnel physically connects to a pipe.…”

Preface Special Issue “Advances in Numerical Modelling of Hydrodynamics”

“…Numerical results are validated against exact linear wave solutions and laboratory experiments of artificially driven waves in the Hele-Shaw tank.  Time step enlargement of an explicit finite volume shallow water model: Explicit numerical methods, although dictate small time steps due to a Courant-Friedrich-Lewy (CFL) stability condition < 1, remain undoubtedly one of the most popular approaches in solving for unsteady shallow water flows (Morales-Hernández et al 2013). In this issue, Morales-Hernandez et al extend their approach for relaxing the CFL condition to > 1 to enable larger time steps in solving the inviscid shallow water equations on unstructured triangular meshes.…”

The analytic solution of the Shallow-Water Equations with partially open sluice-gates: The dam-break problem

“…This procedure, similar to that adopted by Zhao et al (1994), can be simply called the equilibrium approach of the sluice-gate internal boundary condition. The criterion used to distinguish between free and submerged flow conditions represents a major difference from the algorithm by Morales-Hernàndez et al (2013).…”

“…Test 7 demonstrates that the algorithm for the calculation of the fluxes through the gate should be The fix introduced by the modified step f2 mod represents a major difference between the scheme considered here and the schemes presented in the literature available (Zhao et al 1994, Natale et al 2004, Catella and Bechi 2006, Morales-Hernàndez et al 2013). Test 7 was repeated using the modified algorithm, and the results of the run with NV = 100 finite volumes are shown in Figure 12a, while the results obtained with NV = 1000 finite volumes are plotted in Figure 12b.…”

“…Reichstetter and Chanson (2013) considered the rarefaction wave generated by the sudden and complete removal of a gate that was partially open at the beginning of the transient. Morales-Hernàndez et al (2013) supplied the construction of the one-dimensional dam-break solution for the case of partial opening of the gate and formation of submerged flow conditions. For all these solutions, good agreement was found between the analytic results and the laboratory experiments (Montuori and Greco 1973, Kubo and Shimura 1981, Yamada 1992, Reichstetter and Chanson 2013, showing that the Shallow-Water…”