Abstract This paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector circular ring shaped bar. The homogeneous elastic wedge-shaped strengthened by on its curved boundary surfaces thin isotropic shells. An analytical method presented to obtain Prandtl’s stress function, torsional rigidity and shearing stresses. A numerical example ill...

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...

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 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...

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...

Determining the shear stress of a structural element caused by torsion is vital problem. The analytical solution Saint-Venant only suitable for simple cross-sections. numerical method to evaluate complicated cross-sections indispensable. Many methods have been studied scientists. Among these studies, Gruttmann proposed an excellent method, which inherited theory. However, use isoparametric four...

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...