This paper deals with the stability study of Partial Differential nonlinear Equation (PDE) of Saint-Venant. The proposed approach is based on the Multi-Models concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows to describe the dynamic of this nonlinear system in infinite dimension over a wide operating range. A st...

Abstract Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range industrial processes. One way to study these stresses through cantilever experiment, whereby thin film deposited onto surface plate that clamped at one end wall. The are generated during drying transmitted and drive bending. Mathematical modelling enables be inferred from mea...

In this communication we analyze the nonlinear stability of pseudo-rigid motions constituted by similarity transformations which leave a point of the mechanical systems fixed. For this we apply the energy-momentum method to a class of relative equilibria formed by upright motions of a deformable Lagrangian top modelled by a Saint Venant-Kirchhoff material.

We provide a new framework for analyzing the flow of an axisymmetric liquid film flowing down vertical fiber, applicable to fiber coating flows and those in similar geometries heat exchangers, water treatment, desalination processes. The problem considered is that viscous falling under influence gravity surface tension on solid cylindrical fiber. Our approach different from existing ones we der...

The research aims are to develop a methodology and the choice of initial formulas for calculating channel deformations in lower reaches waterworks on rivers composed easily eroded soils (like Amu Darya river). To calculate total erosion below Mezhdurechensk reservoir, both theoretical equations deformation (Saint-Venant equations) empirical dependences transporting capacity flow (turbidity) mor...

We consider the extension of momentum conservative staggered-grid (MCS) scheme for flow simulation in channels with varying depth and width. The is formulated using properties Saint-Venant equations. proposed was successful handling various steady flows achieved results that are complete accordance analytical solutions. Different choices boundary conditions have created solutions according to m...

Hydraulic engineering studies related to floods usually require the lateral distribution of flow velocity across the compound channel section, constituted by the main channel and the floodplain. 2D-Horizontal numerical models (such as the public domain software RMA2 of USACE) are now broadly accepted as an appropriate theoretical model to solve this problem. However, as in the majority of appli...

The problem of numerical determination Lyapunov-stable (exponential stability) solutions the Saint-Venant equations system has remained open until now. authors this paper previously proposed an implicit upwind difference splitting scheme, but its practical applicability was not indicated there. In paper, is solved successfully, namely, algorithm for calculating developed and implemented using s...

In this paper, we address the problem of exponential stability density-velocity systems with boundary conditions. Density-velocity are typical hyperbolic that omnipresent in physics as they encompass all consist a flux conservation and momentum equation. paper show any such system can be stabilized exponentially quickly H 2 norm using simple local feedbacks, provided condition on source term is...

This paper describes, from a theoretical point of view, the appearance and characteristics granular roll waves in chute flow, maximal size these can attain for given influx material into system. Granular are steady travelling wave solutions generalized Saint-Venant equations flowing matter, appearing when Froude number $Fr$ incoming flow exceeds critical value, $Fr>Fr_{cr}$ . We focus upon p...