In order to minimize the catastrophic effects of floods, it is essential to have good forecasts of the flood dynamics. To carry out these forecasts, commercial computing tools use hydraulic models based on the Saint-Venant equations. Instead of these hydraulic models, this paper proposes the use of input-output adaptive predictive expert (APE) models with properly adjusted parameters. For the i...

We study the inviscid multilayer Saint-Venant (or shallow-water) system in the limit of small density contrast. We show that, under reasonable hyperbolicity conditions on the flow and a smallness assumption on the initial surface deformation, the system is well-posed on a large time interval, despite the singular limit. By studying the asymptotic limit, we provide a rigorous justification of th...

We present the Lie symmetry analysis for a hyperbolic partial differential system known as one-dimensional Saint-Venant-Exner model. The model describes shallow-water systems with bed evolution given by Exner terms. sediment flux is considered to be power-law function of velocity fluid. admitted symmetries are classified according power index flux. Furthermore, optimal determined in all cases. ...

We give several examples of modeling in nonlinear elasticity where a quasiconvexification procedure is needed. We first recall that the three-dimensional Saint Venant-Kirchhoff energy fails to be quasiconvex and that its quasiconvex envelope can be obtained by means of careful computations. Second, we turn to the mathematical derivation of slender structure models: an asymptotic procedure using...

Due to computational issues associated with the free surface NavierStokes or Euler equations, the simulations of geophysical flows are often carried out with shallow water type models of reduced complexity. Thus the hydrostatic assumption for shallow water flows leads to non-linear hyperbolic systems of Saint-Venant type [1]. For these vertically averaged models, efficient and robust numerical ...

English version: Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in [1], coupled with a positive numerical flux, allows to verify important mathematical and physical properties like the positivity of the water height and, thus, to avoid unstabilities when dealing wi...

A parameter identification problem for systems governed by first-order, linear hyperbolic partial differential equations subjected to periodic forcing is investigated. The problem is posed as a PDE constrained optimization problem with data of the problem given by the measured input and output variables at the boundary of the domain. By using the governing equations in the frequency domain, a s...

An optimal flow control methodology based on adjoint sensitivity analysis for controlling nonlinear open channel flows with complex geometries is presented. The adjoint equations, derived from the nonlinear Saint-Venant equations, are generally capable of evaluating the time-dependent sensitivities with respect to a variety of control variables under complex flow conditions and cross-section sh...

flood flow importance enforces we to simulate its components exactly. in this study, saint-venant equations in conservative form are usedto simulate one-dimensional rapidly varied flow in the river. upstream methods of godunov family in finite volume frame work are used to numerical solution. according to flow conditions in the river, the equations used are included in the source term of the be...