A Non-Equilibrium Sediment Transport Model for Dam Break Flow over Moveable Bed Based on Non-Uniform Rectangular Mesh

A 3D investigation of sediment transport processes across long, straight channels exposed to an oblique incoming current is presented. For this purpose a detailed mathematical flow and sediment transport model is applied. The governing flow and sediment transport equations are solved in a curvilinear coordinate system. The sediment transport model is composed of bed and suspended load, applying a convection-diffusion equation for the latter. As the flow crosses a channel obliquely, it is refracted toward the channel alignment. The effect of the current refraction on the sediment transport is studied using both 2D (depth-averaged) and 3D models. Shortcomings of models based on depth-averaged descriptions are underlined through comparison with the 3D model. A reliable description of the backfilling process requires a flow and sediment transport model capable of capturing the following aspects: (1) The direction and magnitude of the bed-shear stress; and (2) the adaptation of suspended sediment to local sediment transport capacities. Calculations of the morphological development of small-scale excavations (e.g., pipeline trenches) exposed to an oblique incoming current are presented.

This work presents the development and calibration of a two dimensional river flow, sediment transport and bed evolution model that couples the active-layer and multiple size-class approach for sediment transport modeling with an enhanced advection algorithm. The governing equations are solved using the fractional step method. This resulted in three successive steps (advection, diffusion and continuity) for the flow equations, and two steps (advection and diffusion) for the sediment transport and bed evolution equations. The focus of the research is the improvement of the advection computation (both in water and sediment computation) by reducing the limitation it imposes on the time step. Overcoming this restriction is enabled by introducing modifications to the characteristic method. Implementing these adjustments allows the characteristic curve to extend throughout multiple computational cells. After evaluating the advection computation for both flow and sediment transport by comparison of the proposed algorithm with various classical methods, the developed model is assessed using field measurements conducted on the Danube River. Analysis of the measured and computed values confirmed the developed model’s reliability.

Quasi-3D two-phase model for dam-break flow over movable bed based on a non-hydrostatic depth-integrated model with a dynamic rough wall law

Understanding processes controlling sediment transports at the mouth of a highly energetic inlet system (San Francisco Bay, CA)

Numerical study of the dam-break flood over natural rivers with macroscopic rocks on movable beds

This paper presents a non-capacity coupled model of dam-break induced geomorphic flows which couples hydrodynamic model, morphodynamic model and bed evolution. An upwind Godunov-type scheme with a modified Roe’s Riemann Solver is implemented to solve the hyperbolic system. As the key closure equation for non-equilibrium sediment transport model, a wide range of previous empirical, semi-empirical or theoretical entrainment functions are summarized and their performance is investigated by application to three dam-break flow cases with a range of different Shields’ parameters. The sensitivity of the parameters in the entrainment formulas is also evaluated. Many of the existing entrainment formulas have rarely been verified thoroughly due to difficulty of validation in the situation of high-magnitude outburst flows. For non-capacity models of dam-break transient flows, an appropriate and applicable entrainment relationship should be selected and applied thoroughly according to different hydraulic conditions.

The mathematical simulation of sediment and Kepone (a highly chlorinated pesticide) transport in the James River estuary was conducted by applying the sediment and contaminant transport model, FETRA, to an 85-km river reach between Bailey and Burwell Bays. The FETRA code is an unsteady, two-dimensional, finite model, utilizing the Galerkin weighted residual method. The model consists of three submodels coupled together to take into account sediment-contaminant interaction. the submodels are: (1) sediment transport model, (2) dissolved contaminant transport model, and (3) particulate contaminant (contaminants adsorbed by sediment) transport model. Transport of sediment and particulate contaminants is simulated for each sediment type or size fraction. The FETRA code was applied to simulate the migration of sediment and Kepone for three river discharges. Tidally influenced depth and velocity distributions in the study area were obtained by the unsteady, one-dimensional code, EXPLORE. These results were used by the two-dimensional code, FETRA, to obtain longitudinal distributions of sediment and Kepone. Hence, the results presented here are cross-sectionally averaged values changing with tidal flow. Comparison of computed results and field data for both sediment and Kepone concentrations indicates very good agreement, confirming the validity of the model. Mathematical simulation of Kepone transport under most probable flow conditions yields an estimate of 89.1 kg/yr of Kepone transported seaward from Burwell Bay. Of this 89.1 kg of total Kepone, 25.3% is carried by sediment, while 74.7% is in a dissolved phase.

A depth-averaged 2-D model has been developed to simulate unsteady flow and nonuniform sediment transport in coastal waters. The current motion is computed by solving the phase-averaged 2-D shallow water flow equations reformulated in terms of total-flux velocity, accounting for the effects of wave radiation stresses and general diffusion or mixing induced by current, waves, and wave breaking. The cross-shore boundary conditions are specified by assuming fully developed longshore current and wave setup that are determined using the reduced 1-D momentum equations. A 2-D wave spectral transformation model is used to calculate the wave height, period, direction, and radiation stresses, and a surface wave roller model is adopted to consider the effects of surface roller on the nearshore currents. The nonequilibrium transport of nonuniform total-load sediment is simulated, considering sediment entrainment by current and waves, the lag of sediment transport relative to the flow, and the hiding and exposure effect of nonuniform bed material. The flow and sediment transport equations are solved using an implicit finite volume method on a variety of meshes including nonuniform rectangular, telescoping (quadtree) rectangular, and hybrid triangular/quadrilateral meshes. The flow and wave models are integrated through a carefully designed steering process. The model has been tested in three field cases, showing generally good performance.

Dike failures due to overtopping frequently occur during floods, causing serious damage to settlements and the environment. For risk management, it is of great importance to understand the mechanisms of dike failure and predict this process accurately. In this study, a three-dimensional numerical model is developed to simulate both overtopping and seepage flows during dike breaching. The governing equations describing the free water flow are extended and applied to simulate also the filtration through porous media. A non-equilibrium sediment transport model is utilized for simulation of the bed deformation. The numerical model is firstly applied to flows over a solid embankment in order to validate the flow part of the model, and then the dike breaching is simulated such that the bed deformation model is also incorporated. By comparison with the experimental results, it is shown that the developed model reproduces overflow and the dike failure processes reasonably well.

A depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow water equations are solved by the SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment transport. The bed load and suspended load are calculated separately or jointly according to sediment transport mode. The sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes. An empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed-load movement direction in channels with steep slopes. Flow and sediment transport are simulated in a decoupled manner, but the sediment module adopts a coupling procedure for the computations of sediment transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement between the simulated results and measured data.

A well-balanced high-resolution shape-preserving central scheme to solve one-dimensional sediment transport equations

Hydrodynamic and sediment transport modeling is important to the analyses of the aggradation and degradation of a river system, the sediment management in a reservoir, and the study of downstream effect on the coastal sediment. This paper presents a development of a three-dimensional hydrodynamic and sediment transport model to investigate the variation of sediment concentration in Shihmen Reservoir in Taiwan under typhoon induced flood events. The fundamental equations that govern fluid flows and sediment concentration are the Reynolds-averaged Navier-Stokes (RANS) equations and sediment transport equation. Model equations are solved by using an implicit, finite-difference scheme in a curvilinear and vertically stretched coordinate system. A case study of Shihmen Reservoir utilizing the present flow and transport model is presented. The upstream flow-rate conditions are obtained from the data recorded during the 2005 Typhoon Haitang. The computed results clearly reflect the three-dimensional feature of the velocity field in the reservoir. The predicted time-varying water surface elevation during the 140-hour flood event agrees well with measured data. For the sediment concentration, only limited measurements in the domain are available. When comparing with the measured data, the present model is capable of providing reasonable predictions on the rising trend of sediment concentration during the period that flow rate increases, however, the model overestimates concentration values at the recession stage when the measurements of sediment concentration are shown in the decreasing trend. Other results showing the time variation of the velocity vectors and sediment concentration at selected vertical layers are presented and discussed.

Vertically-averaged and moment equations for flow and sediment transport

A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in a square is considered. A Neumann condition is specified on one side of the square, and a Dirichlet condition is set on the other three. It is assumed that the coefficient of the equation, its right-hand side, and the boundary values of the desired solution or its normal derivative on the sides of the square are smooth enough to ensure the required smoothness of the solution in a closed domain outside the neighborhoods of the corner points. No compatibility conditions are assumed to hold at the corner points. Under these assumptions, the desired solution in the entire closed domain is of limited smoothness: it belongs only to the Hölder class C μ, where μ ∈ (0, 1) is arbitrary. In the domain, a nonuniform rectangular mesh is introduced that is refined in the boundary domain and depends on a small parameter. The numerical solution to the problem is based on the classical five-point approximation of the equation and a four-point approximation of the Neumann boundary condition. A mesh refinement rule is described under which the approximate solution converges to the exact one uniformly with respect to the small parameter in the L ∞ norm. The convergence rate is O(N −2ln2 N), where N is the number of mesh nodes in each coordinate direction. The parameter-uniform convergence of difference schemes for mixed problems without compatibility conditions at corner points was not previously analyzed.

A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in a square is considered. A Neumann condition is specified on one side of the square, and a Dirichlet condition is set on the other three. It is assumed that the coefficient of the equation, its right-hand side, and the boundary values of the desired solution or its normal derivative on the sides of the square are smooth enough to ensure the required smoothness of the solution in a closed domain outside the neighborhoods of the corner points. No compatibility conditions are assumed to hold at the corner points. Under these assumptions, the desired solution in the entire closed domain is of limited smoothness: it belongs only to the Hölder class C μ, where μ ∈ (0, 1) is arbitrary. In the domain, a nonuniform rectangular mesh is introduced that is refined in the boundary domain and depends on a small parameter. The numerical solution to the problem is based on the classical five-point approximation of the equation and a four-point approximation of the Neumann boundary condition. A mesh refinement rule is described under which the approximate solution converges to the exact one uniformly with respect to the small parameter in the L ∞ norm. The convergence rate is O(N −2ln2 N), where N is the number of mesh nodes in each coordinate direction. The parameter-uniform convergence of difference schemes for mixed problems without compatibility conditions at corner points was not previously analyzed.