A model is presented for the simulation of shallow water flow and, specifically, flood waves propagating on a dry bed. The governing equations are transformed to an equivalent system valid on a deforming coordinate system and are solved by a dissipative finite-element technique. A second-order difference scheme is employed for the integration in time. The implicit nonlinear equations resulting from the weak formulations are solved by the Newton-Raphson method, and the set of linear algebraic equations generated is solved by a frontal algorithm. A deforming grid generation scheme is introduced in the dissipative finite-element formulation to account for the effects of the propagating or receding wave fronts on dry land. The accuracy and stability of the model is examined by comparing the model results with observed data from an experimental field test. Results of trial runs for the simulation of overland flow are also presented.

Closure of "Model for Flood Propagation on Initially Dry Land"

http://sgpwe.izt.uam.mx/files/users/uami/sho/SedimentationTanksDesign.pdf

A CFD methodology for the design of sedimentation tanks in potable water treatment Case study: The influence of a feed flow control baffle

A numerical model for the computation of turbulent flows in sedimentation tanks is presented. Based on a nonorthogonal grid formulation, it can handle fairly arbitrary two-dimensional geometries. It solves the full two-dimensional elliptic governing flow equations with the \Ik\N–ϵ\N turbulence model. Effects on momentum, as well as turbulent kinetic energy balances, due to sediment-induced density currents are taken into account. Solids with a broad settling velocity distribution are treated by considering different settling velocity classes. A simple flocculation model assuming only turbulent shear-induced flocculation is formulated, and the importance of this cause of flocculation is examined. Predicted velocity and concentration profiles and removal efficiencies are compared with observations in a tertiary settling basin in Sweden. Results suggest that the flow field is significantly changed by seemingly small density differences, that shear-induced flocculation is relatively unimportant, and that the influent settling velocity distribution is critical for accurately predicting removal efficiencies.

Density Currents and Shear-Induced Flocculation in Sedimentation Tanks

Flooding due to the failure of a dam or dyke has potentially disastrous consequences. This paper presents a Godunov-type finite volume solver of the shallow water equations based on dynamically adaptive quadtree grids. The Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) scheme is used to evaluate interface fluxes in both wet- and dry-bed applications. The numerical model is validated against results from alternative numerical models for idealized circular and rectangular dam breaks. Close agreement is achieved with experimental measurements from the CADAM dam break test and data from a laboratory dyke break undertaken at Delft University of Technology. Copyright © 2004 John Wiley Sons, Ltd.

Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids

Model for Flood Propagation on Initially Dry Land

The equations governing two-dimensional, steady flow in circular and rectangular primary settling basins are formulated. Mean-flow equations expressing conservation of mass and momentum are combined with a two-equation turbulence model (k-ϵ model) to compute velocity fields in sedimentation basins. The turbulence is characterized by a turbulent kinematic eddy viscosity which is computed directly as part of the solution. A numerical solution to the mathematical model is formulated by application of the Galerkin finite element method to the equation residuals. The resulting non-linear system of equations is solved by a variation of Newton's method. The model is applied to predict the flow pattern in a rectangular settling basin. A vector plot of the basin velocity field and contour plot of the turbulent kinematic eddy viscosity are presented.

Numerical Analysis of Flow in Sedimentation Basins

Mathematical models based on the Saint-Venant equations for open channel flow often encounter serious difficulties when applied to natural channels. On the other hand, the approximate flood routing models used in practice may yield results which are in gross error. In this work five mathematical models are constructed based on equations ranging from the complete dynamic system to a simple normal-depth kinematic wave equation. The results of the models are compared between themselves and with experimental data, in the form of free-surface profiles and stage hydrographs. The models are then converted to dimensionless form, which reduces the number of independent parameters controlling their solution. The results of these calculations are presented in the form of dimensionless plots of maximum flood depth and time versus distance along the channel, for various levels of truncation of the open-channel flow equations. Estimates for the permissible range of application of the simplified routing models are given, and recommendations are made for their judicious application.

Applicability of Dam‐Break Flood Wave Models

A theory is presented for flow through a partial dam failure. The breach section is treated as an internal boundary condition which interrupts the continuous long wave occurring upstream and downstream of the dam. At the breach section, basic equations of mass, momentum, and energy conservation are formulated in terms of depths and velocities occurring immediately upstream and downstream of the dam. These equations are coupled with the long time solution of the unsteady flow equation via appropriate characteristic relations emanating from the breach. Three modes of solutions are identified in the present theory depending on whether the breach section is submerged or acts as a control. Numerical solutions are presented based on a characteristic model and a difference scheme of the predictor-corrector type. Computational results for these models are presented and compared with experimental data.

One-dimensional models for partially breached dams

The equation governing the concentration field for a dilute suspension of particles is presented for flow in circular and rectangular primary settling basins. The formulation is valid for two‐dimensional, mean steady, isothermal, turbulent flow conditions. Basin flow velocities are obtained from a hydrodynamic model which determines the turbulent diffusion coefficients for mass transport as part of the overall solution. A numerical solution to the mathematical model is formulated by application of the Galerkin finite element method to the equation residuals. The resulting linear, algebraic equation set is solved by a standard elimination scheme. Results include contour plots of particle concentration fields for rectangular and circular basins and removal efficiencies for these tanks. The effect of partial resuspension at the bed (deposition retarded) is included in the analysis.

David R. Schamber

Papers

Numerical Analysis of Flow in Sedimentation Basins

Applicability of Dam‐Break Flood Wave Models

One-dimensional models for partially breached dams

Particle Concentration Predictions in Settling Basins

Closure to “Particle Concentration Predictions in Settling Basins” by David R. Schamber and Bruce E. Larock (June, 1983)