A family of Godunov-type central-upwind schemes for the Saint-Venant system of shallow water equations has been first introduced in [A. Kurganov and D. Levy, M2AN Math. Model. Numer. Anal., 36, 397-425, 2002]. Depending on the reconstruction step, the second-order versions of the schemes there could be made either well-balanced or positivity preserving, but fail to satisfy both properties simul...

A generalization of the discrete linear cascade model (DLCM), which is a statespace-formulated discretized version of the continuous Kalinin–Milyukov–Nash Cascade, is described for noninteger number of uniform storage elements. The generalized model was tested against numerically integrated values of the Saint-Venant equations and was found to yield improved model accuracy in comparison with th...

In this paper, details of a conjunctive surface–subsurface numerical model for the simulation of overland flow are presented. In this model, the complete onedimensional Saint-Venant equations for the surface flow are solved by a simple, explicit, essentially non-oscillating (ENO) scheme. The two-dimensional Richards equation in the mixed form for the subsurface flow is solved using an efficient...

Below-grade stormwater storage tunnels are designed to provide relief for collection networks during intense rain events. Air must be evacuated as the tunnel fills and, depending on the system geometry, the air may become pressurized. This research presents an investigation on various ways that the air pressurization influences the water flow. The investigation used an experimental apparatus co...

A positive surge results from a sudden change in flow that increases the depth. It is the unsteady flow analogy of the stationary hydraulic jump and a geophysical application is the tidal bore. Positive surges are commonly studied using the method of characteristics and the Saint-Venant equations. The article presents the results from new experimental investigations conducted in a large rectang...

We are interested in simulating blood flow in arteries with a one dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint-Venant/ shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme which were not previously considered. To emphasize the necessity of thi...

This paper proposes the use of predictive optimal control as a suitable methodology to manage efficiently transport water networks. The predictive optimal controller is implemented using MPC control techniques. The Arrêt-Darré/Arros dam-river system located in the Southwest region of France is proposed as case study. A high-fidelity dynamic simulator based on the full Saint-Venant equations and...

The stability problem of a system of conservation laws perturbed by non-homogeneous terms is investigated. These non-homogeneous terms are assumed to have a small C1-norm. By a Riemann coordinates approach a sufficient stability criterion is established in terms of the boundary conditions. This criterion can be interpreted as a robust stabilization condition by means of a boundary control, for ...

We propose a new two-dimensional numerical scheme to solve the Saint-Venant system of shallow water equations in the presence of partially flooded cells. Our method is well-balanced, positivity preserving, and handles dry states. The latter is ensured by using the draining time step technique in the time integration process, which guarantees non-negative water depths. Unlike previous schemes, o...