Maurizio Venutelli

Analysis of Dynamic Wave Model for Unsteady Flow in an Open Channel

The models for flood propagation in an open channel are governed by Saint-Venant’s equations or by their simplified forms. Assuming the full form of hyperbolic type nonlinear expressions, the complete or dynamic wave model is obtained. Hence, after first-order linearization procedure, the dispersion relation is obtained by using the classical Fourier analysis. From this expression, the phase and group speed and the variations of the amplitude of the waves are defined and investigated. Adopting Manning’s resistance formula, the effects of the variations of the Froude number, Courant number, and friction parameter are examined in the wave number domain for progressive and regressive waves. For small and high wave numbers, the simplified kinematic and gravity wave models are recovered, respectively. Moreover, the analysis confirms, according to the Vedernikov criterion, the Froude number value corresponding to the stability condition to contrast the development of roll waves. In addition, for stable flow on ...

Time-stepping Padé-Petrov-Galerkin models for hydraulic jump simulation

Four Pade-Petrov-Galerkin models, for numerical computation discontinuous flow in open channels, are proposed in this work. Time discretization, in multi-stage approach of Saint-Venants basic equations, is obtained by first- and second-sub-diagonal L-stable Pade approximations in factorized form, whereas the spatial discretization is obtained by the standard Petrov-Galerkin finite element method, with two parameters cubic weight functions. The accuracy of the time-stepping models, formulated in the explicit stages by the unknown mass matrix in lumped form, is investigated by von Neumanns classical analysis. Then, the adjustment parameter values of the weight functions are obtained in order to give a second-order accuracy to the schemes. Finally, the resulting models produce a clean, sharp jump structure that agrees favorably with the exact solution of the test problems in frictionless and friction channels.

A third-order explicit central scheme for open channel flow simulations

A third-order explicit time-stepping model for the simulations in open channels flow is presented. The time discretization of one-dimensional Saint- Venants basic equations is obtained by Taylor series expansion, formulated in multi-stage approach, whereas the spatial discretization is obtained by finite difference central scheme. First- and second-order models have been obtained by using piecewise constant and piecewise linear MUSCL (monotone upwind scheme for conservation laws) approximations. Afterwards, the third-order model proposed is obtained by a piecewise quadratic polynomial approximation. Using Fouriers linear analysis, the stability and the accuracy of the scheme are investigated. The numerical results, for predicting dam-break in a horizontal and frictionless channel and for the representation of the hydraulic jump in prismatic and non-prismatic channels, with non-uniform bottom slope, are evaluated, and compared with the corresponding analytical and measured solutions.

A third-order Taylor–Galerkin model for the simulation of two-dimensional unsteady free surface flows

Abstract A Taylor–Galerkin third-order method is presented to integrate the equations describing two-dimensional, unsteady flows having a free surface. The discretization in time, with Taylor series expansions, is based on a fractional step, while the spatial approximation is obtained by the conventional Galerkin finite element method. Results are presented, in terms of the water profile history and flow velocity field, for two simulations: a partial and sudden breakage of a dam in a horizontal and frictionless river-bed, and the flow through a channel contraction.