We consider a tank containing a fluid. The tank is subjected to directly controlled translations and rotations. The fluid motion is described by linearized wave equations under shallow water approximations. For irrotational flows, a new variational formulation of Saint-Venant equations is proposed. This provides a simple method to establish the equations when the tank is moving. Several control...

The Serre–Green–Naghdi (SGN) equations, also known as the fully-nonlinear Boussinesq wave equations, accurately describe the behaviour of dispersive shoaling water waves. This article presents and validates a novel combination of methods for the numerical approximation of solutions to the SGN equations. The approach preserves the robustness of the original finite-volume Saint-Venant solver, in ...

The paper deals with output feedback regulation of exponentially stable systems by an integral controller. We have recently proposed appropriate Lyapunov functional to prove exponential stability the closed-loop system. approach is dedicated in this hyperbolic and especially de Saint-Venant equations giving explicitly gains ensure stabilized controller: parameters expression deduced directly ba...

Large-scale floods are one of the major events that impact national economy and people’s livelihood every year during flood season. Predicting factors evolution is a worldwide problem. We use two-dimensional Saint-Venant equations as an example for high-performance computing in modelling behavior. Discretization with initial boundary conditions finite difference method explicit leapfrog scheme ...

We study a simple one-dimensional (1-D) toy model for landslides-generated nonlinear water waves. The landslide is modeled as a rigid bump translating down the side of the bottom while the water motion is modeled by the Saint-Venant system of shallow water equations. The resulting system is numerically solved using a well-balanced positivity preserving central-upwind scheme. The obtained numeri...

This paper deals with the regulation problem of a class of irrigation canals using the Saint-Venant partial differential equations (pde). The Internal Model Boundary Control (IMBC) approach is used and the multireaches case is considered (several reaches in cascade). Perturbation theory of exponential semigroup used for control synthesis is extended here to nonhomogeneous hyperbolic systems, as...

In this paper we construct a numerical solver for the Saint Venant equations. Special attention is given to the balancing of the source terms, including the bottom slope and variable crosssectional profiles. Therefore a special discretization of the pressure law is used, in order to transfer analytical properties to the numerical method. Based on this approximation a wellbalanced solver is deve...