A technical obstruction preventing the conclusion of nonlinear stability of large-Froude number roll waves of the St. Venant equations for inclined thin film flow is the ”slope condition” of Johnson-Noble-Zumbrun, used to obtain pointwise symmetrizability of the linearized equations and thereby high-frequency resolvent bounds and a crucial H nonlinear damping estimate. Numerically, this conditi...

Abstract. We are interested in simulating overland flow on agricultural fields during rainfall events. In this context, we definitely have to cope with dry/wet interfaces and water inflow on dry soil. The model considered is the Shallow Water system (or Saint-Venant equations) without infiltration. Moreover, the model has to be completed with friction terms. It is numerically solved by a finite...

Flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. Floods are taken unsteady flows that vary by time and location. Equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the Saint-Venant hypothesis is considered. Dynamic wave model as ...

We are interested in simulating overland flow on agricultural fields during rainfall events. The model considered is the shallow water system (or Saint-Venant equations) without infiltration, complemented with a friction term. In this context, we definitely have to cope with dry/wet interfaces and water inflow on dry soil. We present a simplified one-dimensional model, discretized with a well-b...

This paper is devoted to nonlinear feedback design for irrigation canals. Such systems are classically described by Saint-Venant nonlinear partial differential equations. Here instead, an ordinary differential equation model (still nonlinear) with a state-dependent input delay is used, on the basis of a model previously proposed in Litrico et al [2003]. The control design approach is based on a...

This paper is concerned with the numerical simulation of the interaction of compressible viscous flow with elastic structures. The flow is described by the compressible Navier-Stokes equations written in the arbitrary Lagrangian-Eulerian (ALE) form. For the elastic deformation we use 2D linear elasticity and nonlinear St. Venant-Kirchhoff and neo-Hookean models. The discretization of both flow ...

Conditions for boundary feedback stabilisability of linear 2×2 hyperbolic systems over a bounded interval are investigated. The main result is to show that the existence of a quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered interval. This result is used to give explicit conditions for the existence of stabilising linear boundary fe...

This article deals with the regulation of water 6ow in open-channels modelled by Saint-Venant equations. By means of a Riemann invariants approach, we deduce stabilizing control laws for a single horizontal reach without friction. The stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general topologies. A control law design base...