Numerical Modeling of Sediment Transport and Bed Evolution in Nonuniform Open-Channel Flows

A one‐dimensional numerical model for simulating unsteady flow and sediment transport in open channels is presented and tested. The flow hydrodynamics is represented by the shallow water equations, and the bed morphodynamics is represented by the Exner equation and an additional equation describing the nonequilibrium sediment transport. Sediment size distribution is represented by the median grain diameter and the standard deviation, instead of the usual modeling with multiple particle size classes. Various methods for computing bed elevation changes at a cross section due to erosion or deposition of sediment are proposed and tested, including an innovative approach that relates the spatial pattern of erosion and deposition rates to boundary shear stress distribution, which is calculated by the Merged Perpendicular Method. An explicit finite difference scheme is employed for solving the water and sediment governing equations. The pertinence of the model is examined for two hypothetical cases. The model is then tested on one set of laboratory experiments on bed degradation under steady flow, showing excellent model data fit, and indicating that incorporating a nonequilibrium sediment transport equation into the model structure is an important element in reproducing the bed degradation process. Finally, the model is applied to simulate the morphological changes taking place in the Ha!Ha! River (Quebec) after the failure of the Ha!Ha! Dyke on July 1996. Relevant results can be obtained in terms of changes in longitudinal bed profile and cross‐sectional geometry as well as water levels, although some discrepancies are obtained between the simulated and surveyed cross‐sectional geometries, mainly because bank failure and channel widening are not modeled.

Mountain watersheds recently burned by wildfire often experience greater amounts of runoff and increased rates of sediment transport relative to similar unburned areas. Given the sedimentation and debris flow threats caused by increases in erosion, more work is needed to better understand the physical mechanisms responsible for the observed increase in sediment transport in burned environments and the time scale over which a heightened geomorphic response can be expected. In this study, we quantified the relative importance of different hillslope erosion mechanisms during two postwildfire rainstorms at a drainage basin in Southern California by combining terrestrial laser scanner‐derived maps of topographic change, field measurements, and numerical modeling of overland flow and sediment transport. Numerous debris flows were initiated by runoff at our study area during a long‐duration storm of relatively modest intensity. Despite the presence of a well‐developed rill network, numerical model results suggest that the majority of eroded hillslope sediment during this long‐duration rainstorm was transported by raindrop‐induced sediment transport processes, highlighting the importance of raindrop‐driven processes in supplying channels with potential debris flow material. We also used the numerical model to explore relationships between postwildfire storm characteristics, vegetation cover, soil infiltration capacity, and the total volume of eroded sediment from a synthetic hillslope for different end‐member erosion regimes. This study adds to our understanding of sediment transport in steep, postwildfire landscapes and shows how data from field monitoring can be combined with numerical modeling of sediment transport to isolate the processes leading to increased erosion in burned areas.

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 3D numerical model for calculating flow and sediment transport in open channels is presented. The flow is calculated by solving the full Reynolds-averaged Navier-Stokes equations with the k − ε turbulence model. Special free-surface and roughness treatments are introduced for open-channel flow; in particular the water level is determined from a 2D Poisson equation derived from 2D depth-averaged momentum equations. Suspended-load transport is simulated through the general convection-diffusion equation with an empirical settling-velocity term. This equation and the flow equations are solved numerically with a finite-volume method on an adaptive, nonstaggered grid. Bed-load transport is simulated with a nonequilibrium method and the bed deformation is obtained from an overall mass-balance equation. The suspended-load model is tested for channel flow situations with net entrainment from a loose bed and with net deposition, and the full 3D total-load model is validated by calculating the flow and sediment transport in a 180° channel bend with movable bed. In all cases, the agreement with measurements is generally good.

The mutual feedback between the swash zone and the surf zone is known to affect large-scale morphodynamic processes such as breaker bar migration on sandy beaches. To fully resolve this feedback in a process-based manner, the morphodynamics in the swash zone and due to swash-swash interactions must be explicitly solved, e.g., by means of a wave-resolving numerical model. Currently, few existing models are able to fully resolve the complex morphodynamics in the swash zone, and none is practically applicable for engineering purposes. This work aims at improving the numerical modelling of the intra-wave sediment transport on sandy beaches in an open-source wave-resolving hydro-morphodynamic framework (e.g., non-hydrostatic XBeach). A transport equation for the intra-wave suspended sediment concentration, including an erosion and a deposition rate, is newly implemented in the model. Two laboratory experiments involving isolated waves and wave trains are simulated to analyse the performance of the model. Numerical results show overall better performance in simulating single waves rather than wave trains. For the latter, the modelling of the morphodynamic response improves in the swash zone compared with the existing sediment transport modelling approach within non-hydrostatic XBeach, while the need of including additional physical processes to better capture sediment transport and bed evolution in the surf zone is highlighted in the paper.

Predicting transport rates is difficult for the morphological features of marine, river, and coastal ecosystems. To design a model bed load sediment transport rate along with the surface layer, a mesh-based numerical method is used, and for the sediment transport the governing equations are employed and depth-averaged is used to create open channel flow and in three-dimensional horizontal space the evaluation is performed. By utilizing the governing equations, the open channel flow discretization and the numerical hydrodynamic model of sediment transport rate are calculated, and in the flow channel by using the solution method the settling velocity is determined. The complex issues involved nonlinear equations for the numerical modelling with solution methodology. The chicken swarm optimization algorithm is revealed by multi-objective metaheuristics optimization, and a better outcome is acquired by optimization. Finally, if polygonal mesh modelling is used in the diversion flow channel and curved bend channel, several experimental models were employed in the model experiments. A numerical measured and improved model is used to estimate the results in comparison, and the optimally developed model forecast rates with accuracy. In some open-channel flows such as reservoirs and rivers, the struggling flow and bed load sediment transport were dealt with in this model. Based on the results obtained, the proposed technique demonstrates significant improvements in both accuracy and prediction performance compared to the existing techniques. The proposed technique achieves an accuracy of 96.87%, outperforming the BCNN technique with an accuracy of 89.77% and the H-ANN-FA technique with an accuracy of 84.65%. Moreover, the proposed technique exhibits a lower RMSE value of 0.12, indicating a substantial reduction in the average deviation between predicted and observed values. Based on the NSE and R2 results, the proposed technique demonstrates remarkable improvements in prediction accuracy compared to the other techniques. The proposed technique achieves an NSE value of 0.998 and R2 value of 0.99, compared to the existing technique with an improvement of 46.47% and 11.24%.

Numerical modelling of the suspended sediment transport in Torres Strait

Bed load transport is an important process in maintaining balance and stabilising channel geometry for restoring the form and function of river ecosystems. The amount and spatial distribution of bed load sediment particles contribute significantly to riverbed level changes. The prediction of bed load sediment transport evolution is an important aspect of catchment planning. This work can be effectively supported through numerical simulation by detailed analyses of flow components and sediment transport inside watersheds. The purpose of this research is to develop a twodimensional depth-averaged numerical model for flow and sediment transport using eight bed load transport equations to predict the time variation of bed deformation in steep slope, torrents and mountain river areas. The two-dimensional depth-averaged shallow water equations, along with the sediment continuity equation, are solved by using the Marker and Cell explicit scheme. Applying the eight bed load transport formulas to both ADM and MLSHM experimental flumes. After we will choice to the most appropriate formula to simulate the bed load transport rate and bed elevation change in the Yang yang mountains river in South Korea. The differences found between the measured experimental data and the numerical simulation for both flow and the time variations of bed deformation showed that the numerical model used in this research is useful for the analysis and prediction of riverbed level variations.

Studying the sediments and predicting the coastal morphological changes have wide applications in coastal engineering, including coastal management, operation, and design of the structures as well as their maintenance, development, and expansion of coasts and coastal structures, which are of paramount importance. This study aims to model the shoreline changes around the Jazireh-e Shomali-Jonoubi Port, calculate the amount of advancement and recession due to the construction of the breakwater, and to determine the areas exposed to erosion and sedimentation. To this end, a series of primary information, including aerial and satellite images, hydrographic and topographic maps, and the specifications and grading of the sediment of the considered coast, has been collected and the overall morphology of the area has been determined. The input data into the model include a 12-year time series of the wave (height, period, and direction of the wave) and the wave climate. The length of the shoreline is 4 km and a profile perpendicular to the coast with a length of 1500 m has been applied to the model. Finally, using numerical modeling, the net and gross potential rates of annual and cumulative sediment transport, as well as shoreline changes after 12 years, were simulated. The effect and length of sedimentation behind the port’s breakwater after 1, 5, 10 and 12 years are 81, 190, 247 and 267 meters, respectively, which is in good agreement with the actual observations. Because the length of the breakwaters is 300 meters, the sedimentation problem has not yet been established for the port after 12 years.

The predictive capability of a three-dimensional (3D) numerical model for sediment transport and resulting scour around a structure is investigated in this study. Starting with the bed-load and suspended-load sediment transport (reference) model developed by Takahashi et al. (2000, “Modeling Sediment Transport Due to Tsunamis With Exchange Rate Between Bed Load Layer and Suspended Load Layer,” Proceedings of the 27th International Conference on Coastal Engineering, ASCE, Sydney, Australia, pp. 1508–1519), we first introduce an extension to incorporate Nielsen’s modified Shields parameter to account for the effects of infiltration/exfiltration flow velocity across the fluid-sand interface on the sediment transport (the modified Shields-parameter model). We then propose a new model to include the influence of the effective stress to account for the stress fluctuations inside the surface layer of the sand bed (the effective-stress model). The three analytical models are incorporated into a 3D numerical solver developed by Nakamura et al. (2008, “Tsunami Scour Around a Square Structure,” Coast. Eng. Japan, 50(2), pp. 209–246) to analyze the dynamics of fluid-sediment interaction and scour. Their solver is composed of two modules, namely, a finite-difference numerical wave tank and a finite-element coupled sand-skeleton pore-water module. The predictive capability of the three alternative coupled models is calibrated against hydraulic experiments on sediment transport and resulting scour around a fixed rigid structure due to the run-up of a single large wave in terms of the sediment transport process and the final scour profile after the wave run-up. It is found that, among the three models considered, the proposed effective-stress model most accurately predicts the scouring process around the seaward corner of the structure. The results also reveal that the deposition and erosion patterns predicted using the effective-stress model are in good agreement with measured results, while a scour hole at the seaward corner of the structure cannot be always predicted by the other two models.

Management and development of water bodies is vital for meeting domestic, agricultural, energy and industrial needs. To that end, dams, artificial channels, lakes and other water structures have been constructed. Management and development of these structures encounter problems of land erosion, reservoir silting, and degradation and aggradation of channel beds, which need to be addressed. Fundamental to these problems are sediment transport, erosion and deposition. Numerical modeling of sediment transport is the best tool to simulate sediment transport in a water body. This study develops a vertically integrated two-dimensional numerical sediment transport model. Sediment transport is simulated in two parts in this model: suspended load and bed load. A fractional step approach is used to solve the two-dimensional advection diffusion equation, which splits the advection-diffusion equation in to two separate parts: advection and diffusion. High resolution conservative algorithm is used to solve the advection part and a semi implicit finite difference scheme is used to solve the diffusion part. Different parallel numerical solvers are developed to solve linear system of equations resulting from diffusion part. Non-uniformity in sediment mixture which is quite common in real world problems is considered. The model is tested for different analytical and laboratory test cases. The model is coded for parallel computers so that enormous power of parallel computers can be exploited.

The purpose of the present paper is to introduce a simple two-part multi-phase model for the sediment transport problems based on the incompressible smoothed particle hydrodynamics (ISPH) method. The proposed model simulates the movement of sediment particles in two parts. The sediment particles are classified into three categories, including the motionless particles, moving particles behave like a rigid body, and moving particles with a pseudo fluid behavior. The criterion for the classification of sediment particles is the Bingham rheological model. Verification of the present model is performed by simulation of the dam break waves on movable beds with different conditions and the bed scouring under steady flow condition. Comparison of the present model results, the experimental data and available numerical results show that it has good ability to simulate flow pattern and sediment transport.

Sediment concentration distributions are predicted in a fully developed open channel flow with a fixed, rough bottom for various types of sediment material. Calculations are done using the k-e turbulence model and relating the mass transfer coefficient to the turbulent eddy-viscosity distribution which is also calculated as a part of the solution. Deposition and entrapment of the sediment particles are considered. Influence of various hydraulic parameters on the predicted sediment concentration are investigated. Predictions are compared with experiments. The results show that concentration distributions can be predicted adequately with the calculated velocity and eddy-viscosity distributions.

A numerical model of nearshore waves, currents, and sediment transport

Numerical model is a useful tool in studying the flow and sediment transport, change in river bed and is built on solving governing differential equations. Numerical model has many different levels and three-dimensional model is the highest level, allowing detailed simulation of flow and sediment transport process in 3D space. The paper presents a method calculating three - dimensional flow and sediment transport in the open channel. Water level and flow velocity are solved from three-dimensional equations with hydrostatic hypothesis. Concentration of suspended sediment, bottom sediment and bottom evolution is solved from transport equations. The governing differential equations in the "sigma" transform coordinate system are solved by finite volume method on unstructured grid of quadrilateral elements. Boundary condition of water level or flow will be imposed on open boundary. For suspended sediment concentrations in the injected phase, suspended sediment concentrations are applied and the outflow phase applies free drainage conditions. This method of calculation was tested with the problem of curved channel sediment transport which was studied experimentally by Odgaard and Bergs. Calculation results are quite consistent with the measured data. In order to test the practical applicability, this method is also tested with the problem of sediment transport in Cu lao Pho islet on Dong Nai river. To solve the matter of hydraulic boundary condition of this problem, the model of Cu lao Pho islet is integrated into the Sai Gon - Dong Nai river system model. Results of the calculation of the river bed evolution of the Cu lao Pho islet on the Dong Nai river also show that this calculation method gives results consistent with the rule and can be used in practical research.