## 1. Introduction

[2] One-dimensional (1-D) hydraulic models are not adequate for natural river flows where the interaction with the floodplains demands more sophisticated approaches. The cost of nonsimplified three-dimensional numerical models can be avoided using depth averaged two-dimensional (2-D) shallow water equations [*Toro*, 2001]. The combination of 2-D models for water flow and regulation structures is rarely found in the literature [*Jaffe and Sanders*, 2001]. This is the main topic of the present work.

[3] When dealing with the shallow water equations, realistic applications always include source terms describing bed level variation and bed friction that, if not properly discretized, can lead to numerical instabilities. In the last decade, the main effort has been put on keeping a discrete balance between flux and source terms in cases of still water, leading to the notion of well-balanced schemes or C property [*Vázquez-Cendón*, 1999; *Toro*, 2001; *Rogers et al*., 2003; *Murillo et al*., 2007]. Recently, in order to include properly the effect of source terms in the weak solution, augmented approximate Riemann solvers have been presented [*George*, 2008; *Rosatti et al*., 2008; *Murillo and García-Navarro*, 2010a]. In this way, accurate solutions can be computed avoiding the necessity of imposing case-dependent tuning parameters, which *Rutschmann* [1994] used frequently to avoid negative values of water depth and other numerical instabilities that appear when including source terms.

[4] The use of floodplain areas connected to the river by levee breaches supplied with control gates can be considered a measure to mitigate floods. Gate opening creates depression waves that interfere with the flood wave to decrease peak flood discharges. This effect may be useful for hazard mitigation.

[5] Regulation algorithms are conventionally used to manage open channel systems. These algorithms consider both an open-channel flow model, rather often formulated according to the 1-D Saint-Venant equations, and a hydraulic model of the check structure [*Buyalski*, 1991]. Using linearization techniques, control algorithms have been developed, designed, and tested [*Litrico and Fromion*, 2009; *Qiao and Yang*, 2010; *Ooi and Weyer*, 2007]. The modeling of gates as inner flow conditions combined with a regulation algorithm makes it possible to consider problems such as flood control [*Young*, 1968], irrigation [*Malaterre and Baume*, 1998] or multireservoir system modeling and management [*Sigvaldson*, 1976; *Kelman et al*., 1989; *Yazicigil et al*., 1983].

[6] The model idealization of the gate operation process is a special case of boundary condition useful for various situations not included in free-surface flow conditions. The gate is formulated to halt the flow when closed and allow free-surface flow and pressurized flow when open. In all cases, the computational cells assigned to the gate location are treated as special cells where boundary conditions have to be imposed. This is not a trivial task in the context of a conservative numerical scheme, and it is precisely the novelty introduced in this work.

[7] This paper first presents the system of equations, the formulation of gate-type internal boundary conditions, and the finite volume scheme. Next, the particular form adopted to formulate the gates as internal boundary conditions is described. A 1-D case of regulation with exact solution is used to analyze the performance of the proposed numerical model in unsteady flow. The possibility to identify flood diversion areas in order to use them as transient storage zones connected to the river by gates can be considered as a risk mitigation tool for the downstream population. An example is provided in the case of the Ebro River (Spain) that justifies the necessity to develop simulation tools able to reproduce scenarios that can be used to improve design of the size and shape of the areas as well as implement the most convenient management of their inundation. In order to simplify this situation, a 2-D benchmark flood regulation test case is presented inspired by the size and characteristics of an Ebro River reach. Dimensional analysis is used to provide insight into the relationships between the dependent and independent variables of the system. In the benchmark case, the effects of gate regulation in floodplain storages area, flooding peak discharge, flood duration, and gate timing are examined. A proportional-integral-derivative (PID) regulation algorithm is implemented as an example that could be used to reduce the peak discharge at the outflow. Finally, the Ebro River reach chosen previously is performed with a simulation of an actual flooding occurred in 2003.