Solving the Saint-Venant equations by numerical methods like finite element and finite difference methods yields an unstable solution for a fairly large open channel. Multiple Knot B-Spline Wavelets (MKBSW) are in the class of semi-orthogonal wavelets that have compact support. Hence, these basis functions are suitable for solving the Saint-Venant equations. However, solving the Saint-Venant eq...

Contents 1. Introduction 2. The two-dimensional models of overland flow 3. The equations of one-dimensional channel flow 4. Simplification of the St. Venant equations 5. Linearization of the St. Venant equations and solution of linear equations 6. Kinematic wave equations and their application 7. Numerical solution of the unsteady flow equations 8 Application of finite elements methods 9. Lumpe...

We investigate the derivation and the mathematical properties of a Saint-Venant model with an energy equation and with temperature-dependent transport coe±cients. These equations model shallow water °ows as well as thin viscous sheets over °uid substrates like oil slicks, atlantic waters in the Strait of Gilbraltar or °oat glasses. We exhibit an entropy function for the system of partial di®ere...

We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Sai...

This paper describes a numerical scheme for approximate the viscous Saint-Venant equations. This scheme is called staggered grid scheme which is a robust, simple and strightforward scheme for viscous SaintVenant equations. Some numerical simulations have been elaborated to validate the accuracy of the scheme, such as the calculation of the convergence rate L1-norm error of the scheme, the compa...

solving a large sparse set of linear equations is of the problems widely seen in every numerical investigation in the entire range of engineering disciplines. employing a finite element approach in solving partial derivative equations, the resulting stiffness matrices would contain many zero-valued elements. moreover, storing all these sparse matrices in a computer memory would slower the compu...

We establish the inviscid limit of the viscous shallow water equations to the Saint-Venant system. For the viscous equations, the viscosity terms are more degenerate when the shallow water is close to the bottom, in comparison with the classical NavierStokes equations for barotropic gases; thus the analysis in our earlier work for the classical Navier-Stokes equations does not apply directly, w...

abstract due to transmission losses and lack of initial flow, flood routing in ephemeral streams is not possible with common methods and it is necessary the flood routing models have been developed for these streams. therefore in this study a computer model for natural river cross section has been developed in that after linearization of partial differential equations of unsteady none uniform f...

Negative surges are caused by a sudden change in flow resulting from a decrease in water depth. New experiments were conducted in a horizontal channel (L = 12 m, W = 0.5 m) to record the unsteady water depth and turbulence in negative surges. The data were collected using video imagery, acoustic displacement meters and acoustic Doppler velocimetry (ADV). The experimental setup was designed to r...

In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resoluti...