the assumptions considered in developing the saint-venant equations limit their application in many practical situations. the modified boussinesq equation was presented to overcome the limitation imposed by saint-venant equation due to the presence of non-hydrostatic pressure distribution and steep slope. in this paper a computational model was developed for solving the modified and the traditi...

The viscous Shallow Water Equations and Quasi-Geostrophic Equations are considered in this paper. Some new terms, related to the Coriolis force, are revealed thanks to a rigorous asymptotic analysis. After providing well-posedness arguments for the new models, the authors perform some numerical computations that confirm the role played by the cosine effect in various physical configurations. Ke...

The aim of this paper is to present a kinetic formulation of a model for the coupling of transient free surface and pressurised flows. Firstly, we revisit the system of Saint-Venant equations for free surface flow: we state some properties of Saint-Venant equations, we propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises (in some ...

We study the exponential stability in H 2 norm of nonlinear Saint-Venant (or shallow water) equations with arbitrary friction and slope using a single proportional-integral (PI) control at one end channel. Using good but simple Lyapunov function we find explicit condition on gain PI to ensure any steady-states. This is independent slope, coefficient, length river, inflow disturbance and, more s...

The hydrodynamic derivation of a variable parameter Muskingum method and its solution procedure for estimating a routed hydrograph were presented in Part I of this series (Perumal, 1994a). In this paper, the limitations of the method, the criterion for its applicability and its accuracy are discussed based on the assumptions used. The method is verified by routing a given hypothetical inflow hy...

In many practical applications of nanotechnology and in microelectromechanical devices, typical structural components are in the form of beams, plates, shells and membranes. When the scale of such components is very small, the material microstructural lengths become important and strain gradient elasticity can provide useful material modelling. In addition, small scale beams and bars can be use...

In this paper, certain well-known upwind schemes for hyperbolic equations are extended to solve the two-dimensional Saint-Venant (or shallow water) equations. We consider unstructured meshes and a new type of nite volume to obtain a suitable treatment of the boundary conditions. The source term involving the gradient of the depth is upwinded in a similar way as the ux terms. The resulting schem...

This article is devoted to the proof of the hydrodynamical limit from kinetic equations (including BGK-like equations) to multidimensional isentropic gas dynamics. It is based on a relative entropy method; hence the derivation is valid only before shocks appear on the limit system solution. However, no a priori knowledge on high velocity distributions for kinetic functions is needed. The case o...