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1.
In order to study the morphological evolution of river beds composed of heterogeneous material, the interaction among the different grain sizes must be taken into account. In this paper, these equations are combined with the two-dimensional shallow water equations to describe the flow field. The resulting system of equations can be solved in two ways: (i) in a coupled way, solving flow and sediment equations simultaneously at a given time-step or (ii) in an uncoupled manner by first solving the flow field and using the magnitudes obtained at each time-step to update the channel morphology (bed and surface composition). The coupled strategy is preferable when dealing with strong and quick interactions between the flow field, the bed evolution and the different particle sizes present on the bed surface. A number of numerical difficulties arise from solving the fully coupled system of equations. These problems are reduced by means of a weakly-coupled strategy to numerically estimate the wave celerities containing the information of the bed and the grain sizes present on the bed. Hence, a two-dimensional numerical scheme able to simulate in a self-stable way the unsteady morphological evolution of channels formed by cohesionless grain size mixtures is presented. The coupling technique is simplified without decreasing the number of waves involved in the numerical scheme but by simplifying their definitions. The numerical results are satisfactorily tested with synthetic cases and against experimental data.  相似文献   

2.
Modelling dam-break flows over mobile beds using a 2D coupled approach   总被引：1，自引：0，他引：1  
Dam-break flows usually propagate along rivers and floodplains, where the processes of fluid flow, sediment transport and bed evolution are closely linked. However, the majority of existing two-dimensional (2D) models used to simulate dam-break flows are only applicable to fixed beds. Details are given in this paper of the development of a 2D morphodynamic model for predicting dam-break flows over mobile beds. In this model, the common 2D shallow water equations are modified, so that the effects of sediment concentrations and bed evolution on the flood wave propagation can be considered. These equations are used together with the non-equilibrium transport equations for graded sediments and the equation of bed evolution. The governing equations are solved using a matrix method, thus the hydrodynamic, sediment transport and morphological processes can be jointly solved. The model employs an unstructured finite volume algorithm, with an approximate Riemann solver, based on the Roe-MUSCL scheme. A predictor–corrector scheme is used in time stepping, leading to a second-order accurate solution in both time and space. In addition, the model considers the adjustment process of bed material composition during the morphological evolution process. The model was first verified against results from existing numerical models and laboratory experiments. It was then used to simulate dam-break flows over a fixed bed and a mobile bed to examine the differences in the predicted flood wave speed and depth. The effects of bed material size distributions on the flood flow and bed evolution were also investigated. The results indicate that there is a great difference between the dam-break flow predictions made over a fixed bed and a mobile bed. At the initial stage of a dam-break flow, the rate of bed evolution could be comparable to that of water depth change. Therefore, it is often necessary to employ the turbid water governing equations using a coupled approach for simulating dam-break flows.  相似文献   

3.
A 2D depth‐averaged hydrodynamic, sediment transport and bed morphology model named STREMR HySeD is presented. The depth‐averaged sediment transport equations are derived from the 3D dilute, multiphase, flow equations and are incorporated into the hydrodynamic model STREMR. The hydrodynamic model includes a two‐equation turbulence model and a correction for the mean flow due to secondary flows. The suspended sediment load can be subdivided into different size classes using the continuum (two‐fluid) approach; however, only one bed sediment size is used herein. The validation of the model is presented by comparing the suspended sediment transport module against experimental measurements and analytical solutions for the case of equilibrium sediment‐laden in a transition from a rigid bed to a porous bed where re‐suspension of sediment is prevented. On the other hand, the bed‐load sediment transport and bed evolution numerical results are compared against bed equilibrium experimental results for the case of a meander bend. A sensitivity analysis based on the correction for secondary flow on the mean flow including the effect of secondary flow on bed shear stresses direction as well as the downward acceleration effect due to gravity on transverse bed slopes is performed and discussed. In general, acceptable agreement is found when comparing the numerical results obtained with STREMR HySeD against experimental measurements and analytical solutions. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

4.
Fully coupled mathematical modeling of turbidity currents over erodible bed   总被引：1，自引：0，他引：1  
Turbidity currents may feature active sediment transport and rapid bed deformation, such as those responsible for the erosion of many submarine canyons. Yet previous mathematical models are built upon simplified governing equations and involve steady flow and weak sediment transport assumptions, which are not in complete accordance with rigorous conservation laws. It so far remains unknown if these could have considerable impacts on the evolution of turbidity currents. Here a fully coupled modeling study is presented to gain new insights into the evolution of turbidity currents. The recent analysis of the multiple time scales of subaerial sediment-laden flows over erodible bed [Cao Z, Li Y, Yue Z. Multiple time scales of alluvial rivers carrying suspended sediment and their implications for mathematical modeling. Adv Water Resour 2007;30(4):715–29] is extended to subaqueous turbidity currents to complement the fully coupled modeling. Results from numerical simulations show the ability of the present coupled model to reproduce self-accelerating turbidity currents. Comparison among the fully and partially coupled and decoupled models along with the analysis of the relative time scale of bed deformation explicitly demonstrate that fully coupled modeling is essential for refined resolution of those turbidity currents featuring active sediment transport and rapid bed deformation, and existing models based on simplified conservation laws need to be reformulated.  相似文献   

5.
1 INTRODUCTIONFor many hydraulic engineering problems, the analysis of flow and bed level variations in openchannels is a fundamental prerequisite. forcal methOds fOr alluvial rivers are well develoPednowadays as far as onediInensional descriPtions are concemed. A cOmPrhensive analysis of Ihe wellknown models is Presented by Habersack(l998). HOwever, for a number of Problems such as channelwidening, flow pattem close to sPuds and etc. a more deailed knowledge of the bed level behavio…  相似文献   

6.
Flow, sediment transport and bed deformation in alluvial rivers normally exhibit multiple time scales. Enhanced knowledge of the time scales can facilitate better approaches to the understanding of the fluvial processes. Yet prior studies of the time scales are based upon the concept of sediment transport capacity at low concentrations, which however is not generally applicable. This paper presents new formulations of the time scales of fluvial flow, suspended sediment transport and bed deformation, under the framework of shallow water hydrodynamics, non-capacity sediment transport and the theory of characteristics for the hyperbolic governing equations. The time scale of bed deformation in relation to that of flow depth is demonstrated to delimit the applicability region of mathematical river models, and the time scale of suspended sediment transport relative to that of the pertinent flow information is analyzed to address if the concept of sediment transport capacity is applicable. For shallow flows with high sediment concentrations, bed deformation may considerably affect the flow and a fully coupled model is normally required. In contrast, for deep flows at low sediment concentrations, a decoupled model is mostly justified. This pilot study of the time scales delivers a new theoretical basis, on which the interaction between flow, suspended sediment transport and bed deformation can be potentially better characterized.  相似文献   

7.
Retrogressive erosion is a high-speed erosion process that usually occurs during the rapid release of stored water in reservoirs built on sandy rivers.Retrogressive erosion has been utilized in the practice of reservoir sedimentation control,but accurate prediction of the bed deformation process by numerical models has rarely been reported.The current study presents a one-dimensional morphodynamic model for simulating the evolution process of retrogressive erosion induced by high-velocity flows on steep slopes.The governing equations apply a Cartesian coordinate system with a vertically oriented z axis.The bed surface gradient and friction terms in the flow equations include correction factors to take account of the effects of high slope on flow movement.The net vertical sediment flux term in the sediment transport and bed deformation equations is calculated using an equation of erosion velocity.Particularly,this equation is based on an empirical relation between the sediment entrainment rate and the Shields parameter in contrast to the traditional sediment transport capacity,and the critical Shields parameter is modified by taking into account the permeability of the sediment layer and the stability of particles on a slope.The feedback of scoured sediment on the flow movement is considered by additional terms in the governing equations.Flume experiments of retrogressive erosion in literature were simulated to validate the model.The temporal variations of the longitudinal profiles of the free surface and channel bed and the sediment transport rate were well predicted.The algorithm calculating sediment entrainment in the proposed model also was validated for an experiment measuring entrainment rate from the literature.More importantly,it was found that the morphodynamic model using the sediment transport capacity equation predicts the trend of cumulative erosion contrary to the measurements,while results of the proposed model can follow a similar trend with the observed data in the retrogressive erosion process.  相似文献   

8.
The fluid-structure interaction curvilinear immersed boundary (FSI-CURVIB) numerical method of Borazjani et al. [3] is extended to simulate coupled flow and sediment transport phenomena in turbulent open-channel flows. The mobile channel bed is discretized with an unstructured triangular mesh and is treated as a sharp-interface immersed boundary embedded in a background curvilinear mesh used to discretize the general channel outline. The unsteady Reynolds-averaged Navier-Stokes (URANS) equations closed with the k − ω turbulence model are solved numerically on a hybrid staggered/non-staggered grid using a second-order accurate fractional step method. The bed deformation is calculated by solving the sediment continuity equation in the bed-load layer using an unstructured, finite-volume formulation that is consistent with the CURVIB framework. Both the first-order upwind and the higher-order hybrid GAMMA schemes [12] are implemented to discretize the bed-load flux gradients and their relative accuracy is evaluated through a systematic grid refinement study. The GAMMA scheme is employed in conjunction with a sand-slide algorithm for limiting the bed slope at locations where the material angle of repose condition is violated. The flow and bed deformation equations are coupled using the partitioned loose-coupling FSI-CURVIB approach [3]. The hydrodynamic module of the method is validated by applying it to simulate the flow in an 180° open-channel bend with fixed bed. To demonstrate the ability of the model to simulate bed morphodynamics and evaluate its accuracy, we apply it to calculate turbulent flow through two mobile-bed open channels, with 90° and 135° bends, respectively, for which experimental measurements are available.  相似文献   

9.
In this study an incompressible smoothed particle hydrodynamics (ISPH) approach coupled with the sediment erosion model is developed to investigate the sediment bed scour and grain movement under the dam break flows. Two-phase formulations are used in the ISPH numerical algorithms to examine the free surface and bed evolution profiles, in which the entrained sediments are treated as a different fluid component as compared with the water. The sediment bed erosion model is based on the concept of pick-up flow velocity and the sediment is initiated when the local flow velocity exceeds a critical value. The proposed model is used to reproduce the sediment erosion and follow-on entrainment process under an instantaneous dam break flow and the results are compared with those from the weakly compressible moving particle semi-implicit (WCMPS) method as well as the experimental data. It has been demonstrated that the two-phase ISPH model performed well with the experimental data. The study shows that the ISPH modelling approach can accurately predict the dynamic sediment scouring process without the need to use empirical sediment transport formulas.  相似文献   

10.
A three-dimensional k-ε-Ap two-fluid turbulence model is proposed to study liquid-particle two-phase flow and bed deformation.By solving coupled liquid-phase and solid-phase governing equations in a finite-volume method,the model can calculate the movement of both water and sediment.The model was validated by water-sediment transport in a 180° channel bend with a movable bed.The validation concerns two-phase time-averaged velocities,bed deformation,water depth,depth-averaged streamwise velocity,cross-stream bed profiles,and two-phase secondary flow velocity vectors.The agreement between numerical results and experimental results was generally good.The comparisons of the numerical results of different models show that the three-dimensional k-ε-Ap two-fluid turbulence model has a relatively higher accuracy than one-fluid model.  相似文献   

11.
The artificial replenishment of sediment is used as a method to re-establish sediment continuity downstream of a dam. However, the impact of this technique on the hydraulics conditions, and resulting bed morphology, is yet to be understood. Several numerical tools have been developed during last years for modeling sediment transport and morphology evolution which can be used for this application. These models range from 1D to 3D approaches: the first being over simplistic for the simulation of such a complex geometry; the latter requires often a prohibitive computational effort. However, 2D models are computationally efficient and in these cases may already provide sufficiently accurate predictions of the morphology evolution caused by the sediment replenishment in a river. Here, the 2D shallow water equations in combination with the Exner equation are solved by means of a weak-coupled strategy. The classical friction approach considered for reproducing the bed channel roughness has been modified to take into account the morphological effect of replenishment which provokes a channel bed fining. Computational outcomes are compared with four sets of experimental data obtained from several replenishment configurations studied in the laboratory. The experiments differ in terms of placement volume and configuration. A set of analysis parameters is proposed for the experimental-numerical comparison, with particular attention to the spreading, covered surface and travel distance of placed replenishment grains. The numerical tool is reliable in reproducing the overall tendency shown by the experimental data. The effect of fining roughness is better reproduced with the approach herein proposed. However, it is also highlighted that the sediment clusters found in the experiment are not well numerically reproduced in the regions of the channel with a limited number of sediment grains.  相似文献   

12.
A three-dimensional k-ε-Ap two-fluid turbulence model is proposed to study liquid-particle two-phase flow and bed deformation. By solving coupled liquid-phase and solid-phase governing equations in a finite-volume method, the model can calculate the movement of both water and sediment. The model was validated by water-sediment transport in a 180° channel bend with a movable bed. The validation concerns two-phase time-averaged velocities, bed deformation, water depth, depth-averaged streamwise velocity, cross-stream bed profiles, and two-phase secondary flow velocity vectors. The agreement between numerical results and experimental results was generally good. The comparisons of the numerical results of different models show that the three-dimensional k-ε-Ap two-fluid turbulence model has a relatively higher accuracy than one-fluid model.  相似文献   

13.
Only comparatively few experimental studies have been carried out to investigate the performance of the HEC-6 river morphological model. The model was developed by the Hydrologic Engineering Center of the US Army Corps of Engineers. In this study, experiments were carried out in a 20 m long concrete flume 0.6 m wide with varying rectangular cross-sections. The channel bed is paved with uniform sand of D50 = 0.9 mm and D90 = 1.2 mm within the test reach of 12 m. Two types of experiments were carried out with sediment transport, one under steady uniform flow and another under steady non-uniform flow conditions. Nine steady uniform flow experiments were carried out to compare the measured equilibrium relationship of flow and sediment transport rate with two bedload formulae, namely, Du Boys and Meyer–Peter and Muller, and with three total load formulae, namely, Toffaleti, Laursen and Yang. It was found that even though the sediment transport consists of a certain portion of bedload, the total load formulae give satisfactory results and better agreement than the two bedload formulae. Five steady non-uniform flow experiments were carried out under various conditions of varying bed profile and channel width and also with sediment addition and withdrawal. The measured transient water surface and bed profiles are compared with the computed results from the HEC-6 model. It was found that the Toffaleti and Yang total load formulae used in the HEC-6 model give the most satisfactory prediction of actual bed profiles under various conditions of non-uniform flow and sediment transport. The effects of Manning's n, variations of sediment inflow, various sediment transport formulae, sediment grain size and the model numerical parameters, i.e. distance interval Δx and numerical weighting factor, on the computed water surface and bed profiles were determined. It was found that the selection of the sediment transport formulae has the most significant effect on the computed results. It can be concluded that the HEC-6 model can predict satisfactorily a long-term average pattern of local scour and deposition along a channel with either a small abrupt change in geometry or gradually varying cross-sections. However, the accuracy of the model prediction is reduced in the regions where highly non-uniform flow occurs.  相似文献   

14.
This numerical investigation was carried out to advance mechanistic understanding of sediment transport under sheet flow conditions. An Euler–Euler coupled two-phase flow model was developed to simulate fluid–sediment oscillatory sheet flow. Since the concentration of sediment particles is high in such flows, the kinematics of the fluid and sediment phases are strongly coupled. This model includes interaction forces, intergranular stresses and turbulent stress closure. Each phase was modeled via the Reynolds-Averaged Navier–Stokes equations, with interphase momentum conservation accounting for the interaction between the phases. The generation and transformation of turbulence was modeled using the two-equation k–εk–ε turbulence model. Concentration and sediment flux profiles were compared with experimental data for sheet flow conditions considering both symmetric and asymmetric oscillatory flows. Sediment and fluid velocity variations, concentration profiles, sediment flux and turbulence parameters of wave-generated sheet flow were studied numerically with a focus on sediment transport characteristics. In all applications, the model predictions compared well with the experimental data. Unlike previous investigations in which the flow is driven by a horizontal pressure gradient, the present model solves the Navier–Stokes equations under propagating waves. The model’s ability to predict sediment transport under oscillatory sheet flow conditions underscores its potential for understanding the evolution of beach morphology.  相似文献   

15.
l INTRODUCTIONThe theories and formulas of sediment dynamics were established based on steady and uniform flows.These theories and formulas often fail to aPply in engineering projects because, in nthee, sediment istransported often by unsteady and non-uniform fiows (Wang et al., l997).TWo cases ofnon-stationarity can be distinguished f long-tertn and short-term (Plate, l994). Long-termnon-stationarity tfansport can be defined as a sediment process which can be treated by sequences ofstat…  相似文献   

16.
We present a two-dimensional vertical (2DV) flow and morphological numerical model describing the behaviour of offshore sand waves. The model contains the 2DV shallow water equations, with a free water surface and a general bed load formula. The water movement is coupled to the sediment transport equation by a seabed evolution equation. Using this model, we investigate the evolution of sand waves in a marine environment. As a result, we find sand wave saturation for heights of 10–30% of the average water depth on a timescale of decades. The stabilization mechanism, causing sand waves to saturate, is found to be based on the balance between the shear stress at the seabed and the principle that sediment is transported more easily downhill than uphill. The migration rate of the sand waves decreases slightly during their evolution. For a unidirectional steady flow the sand waves become asymmetrical in the horizontal direction and for a unidirectional block current asymmetrical in the vertical. A sensitivity analysis showed the slope effect of the sediment transport plays an important role herein. Furthermore, the magnitude of the resistance at the seabed and the eddy viscosity influence both the timescale and height of sand waves. The order of magnitudes found of the time and spatial scales coincide with observations made in the southern bight of the North Sea, Japan and Spain.  相似文献   

17.
《国际泥沙研究》2020,35(4):386-394
Sediment transport simulations are important in practical engineering. In this study, a graphics processing unit (GPU)-based numerical model coupling hydrodynamical and morphological processes was developed to simulate water flow, sediment transport, and morphological changes. Aiming at accurately predicting the sediment transport and sediment scouring processes, the model resolved the realistic features of sediment transport and used a GPU-based parallel computing technique to the accelerate calculation. This model was created in the framework of a Godunov-type finite volume scheme to solve the shallow water equations (SWEs). The SWEs were discretized into algebraic equations by the finite volume method. The fluxes of mass and momentum were computed by the Harten, Lax, and van Leer Contact (HLLC) approximate Riemann solver, and the friction source terms were calculated by the proposed a splitting point-implicit method. These values were evaluated using a novel 2D edge-based MUSCL scheme. The code was programmed using C++ and CUDA, which could run on GPUs to substantially accelerate the computation. The aim of the work was to develop a GPU-based numerical model to simulate hydrodynamical and morphological processes. The novelty is the application of the GPU techniques in the numerical model, making it possible to simulate the sediment transport and bed evolution in a high-resolution but efficient manner. The model was applied to two cases to evaluate bed evolution and the effects of the morphological changes on the flood patterns with high resolution. This indicated that the GPU-based high-resolution hydro-geomorphological model was capable of reproducing morphological processes. The computational times for this test case on the GPU and CPU were 298.1 and 4531.2 s, respectively, indicating that the GPU could accelerate the computation 15.2 times. Compared with the traditional CPU high-grid resolution, the proposed GPU-based high-resolution numerical model improved the reconstruction speed more than 2.0–12.83 times for different grid resolutions while remaining computationally efficient.  相似文献   

18.
INON-EQUILIBRIUMMOVEMENTContinualexchangeremainsamongthebedmaterial,bedloadandsuspendedloadinariver.Thebedloadmovesonthebedsurfaceandjumpsinsteps.Itstransportrateperwidthvarieswithvaryingflowintensity;whilethesuspendedloadmoveswithalongstep,evenifthehydraulicfactorsbecomeweaker,itwillnotretUrntothebeduntilfinishingthefallingprocess.ThismeansthatahysteresisexistsbetWeenthechangeofthesuspendedsedimentmovementandflowvelocity.Foruniformandsteadyflow,thesedimentmovementkeepsinequilibriumi…  相似文献   

19.

In order to simulate the dynamics of fine sediments in short tidal basins, like the Wadden Sea basins, a 1D cross-sectional averaged model is constructed to simulate tidal flow, depth-limited waves, and fine sediment transport. The key for this 1D model lies in the definition of the geometry (width and depth as function of the streamwise coordinate). The geometry is computed by implementing the water level and flow data, from a 2D flow simulation, and the hypsometric curve in the continuity equation. By means of a finite volume method, the shallow-water equations and sediment transport equations are solved. The bed shear stress consists of the sum of shear stresses by waves and flow, in which the waves are computed with a depth-limited growth equation for wave height and wave frequency. A new formulation for erosion of fines from a sandy bed is proposed in the transport equation for fine sediment. It is shown by comparison with 2D simulations and field measurements that a 1D schematization gives a proper representation of the dynamics in short tidal basins.

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20.
In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space–time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.  相似文献   

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