We study the Serre-Green-Naghdi system under a non-hydrostatic formulation, modelling incompressible free surface flows in shallow water regimes. This system, unlike well-known (nonlinear) Saint-Venant equations, takes into account effects of pressure term as well dispersive phenomena. Two numerical schemes are designed, based on finite volume - difference type splitting scheme and iterative co...

The well-balanced, positivity-preserving scheme of Audusse et al, 2004, for the solution of the Saint-Venant equations with wetting and drying, is generalised to an adaptive quadtree spatial discretisation. The scheme is validated using an analytical solution for the oscillation of a fluid in a parabolic container, as well as the classic Monai tsunami laboratory benchmark. An efficient database...

Rating curves relating stream discharge to water-surface stage are traditionally established empirically through many measurements of discharge and concurrent stage. However, discharge measurements typically scatter and do not show a unique relation to the stage because the underlying physics are usually not reflected in the rating. Examining the relationship of stage versus discharge in open c...

Systems of partial differential equations that include the momentum and the mass conservation equations are commonly used for the simulation of debris flow initiation, propagation and deposition both in field and in laboratory research. The numerical solution of the partial differential equations can be very complicated and consequently many approximations that neglect some of their terms have ...

In this paper, the solution of an isotropic hollow cylinder, with an isotropic coating, weakened by multiple radial cracks is studied. The hollow cylinder and its coating are under Saint-Venant torsional loading. The series solution is then derived for displacement and stress fields in the cross section of the cylinder containing a Volterra-type screw dislocation. The dislocation solution is em...

Article history: The 1999 Chi-Chi earthquak Received 22 April 2008 Received in revised form 30 September 2008 Accepted 4 October 2008 Available online xxxx

This paper proposes a new time-scaling approach for computational optimal control of a distributed parameter system governed by the Saint-Venant PDEs. We propose the time-scaling approach, which can change a uniform time partition to a nonuniform one. We also derive the gradient formulas by using the variational method. Then the method of lines (MOL) is applied to compute the Saint-Venant PDEs ...

This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating ...