Modelling dam-break flows over mobile beds using a 2D coupled approach

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.     

A semi-implicit three-dimensional numerical model for non-hydrostatic pressure free-surface flows on an unstructured,sigma grid

A semi-implicit 3-D numerical formulation for solving non-hydrostatic pressure free-surface flows on an unstructured,sigma grid is proposed.Pressure-splitting and 9 semi-implicit methods are inherited and reformed from Casulli’s z-coordinate formulation.The non-orthogonal sigma-coordinate transformation leads to additional terms. The resulting linear system for the non-hydrostatic correction is diagonally dominant but unsymmetric,and it is solved by the BiCGstab method.In contrast with z-coordinate non-hydrostatic models,the new model fits vertical boundaries much better,which is important for the long-time simulation of sediment transport and riverbed deformation.A lock-exchange density flow is computed to determine whether the new scheme is able to simulate non-hydrostatic free-surface flows.The new model is further verified using the field data of a natural river bend of the lower Yangtze River.Good agreement between simulations and earlier research results,field data is obtained, indicating that the new model is applicable to hydraulic projects in real rivers.     

THREE DIMENSIONAL MATHEMATICAL MODEL OF SEDIMENT TRANSPORT IN ESTUARINE REGIONS -A CASE STUDY OF THE HAIHE RIVER MOUTH

1 INTRODUCTIONUnderstanding the flow characters in open channel or other water area, whether natufal water bodies(such as rivers and estuaries) or man-made strUctures (such as navigational channels, harbors), isimportant for addressing numerous hydraulic engineering problems. These include the selechons ofsuitable waste disposal sites, contndnant transport, sediment transport and other ecological problems.The major difficulty for solving these problems is that it often requires an optimal…     

Multi-block lattice Boltzmann simulations of solute transport in shallow water flows

We report a two-dimensional multi-block lattice Boltzmann model for solute transport in shallow water flows, which is developed based on the advection–diffusion equation for mass transport and the shallow water equations for the flows. A weighting factor is included in the centered scheme for improved accuracy. The model is firstly verified by simulating three benchmark tests: wind-driven circulation in a dish-shaped lake, jet-forced flow in a circular basin, and flow formed by two parallel streams containing different uniform concentrations at the same constant velocity; and then it is applied to a practical wind-induced flow, Baiyangdian Lake, which is characterized by irregular geometries and complex bathymetries. The numerical results have shown that the model is able to produce accurate and detailed results for both water flows and solute transport, which is attractive, especially for flows in narrow zones of practical terrains and certain areas with largely varying pollutant concentrations.     

A GPU-based numerical model coupling hydrodynamical and morphological processes

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.     

Curvilinear immersed boundary method for simulating coupled flow and bed morphodynamic interactions due to sediment transport phenomena

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.     

A mass conservative scheme for simulating shallow flows over variable topographies using unstructured grid

Most available numerical methods face problems, in the presence of variable topographies, due to the imbalance between the source and flux terms. Treatments for this problem generally work well for structured grids, but most of them are not directly applicable for unstructured grids. On the other hand, despite of their good performance for discontinuous flows, most available numerical schemes (such as HLL flux and ENO schemes) induce a high level of numerical diffusion in simulating recirculating flows. A numerical method for simulating shallow recirculating flows over a variable topography on unstructured grids is presented. This mass conservative approach can simulate different flow conditions including recirculating, transcritical and discontinuous flows over variable topographies without upwinding of source terms and with a low level of numerical diffusion. Different numerical tests cases are presented to show the performance of the scheme for some challenging problems.     

A Godunov-Type Scheme for Atmospheric Flows on Unstructured Grids: Euler and Navier-Stokes Equations

In recent years there has been a growing interest in using Godunov-type methods for atmospheric flow problems. Godunov's unique approach to numerical modeling of fluid flow is characterized by introducing physical reasoning in the development of the numerical scheme (van Leer, 1999). The construction of the scheme itself is based upon the physical phenomenon described by the equation sets. These finite volume discretizations are conservative and have the ability to resolve regions of steep gradients accurately, thus avoiding dispersion errors in the solution. Positivity of scalars (an important factor when considering the transport of microphysical quantities) is also guaranteed by applying the total variation diminishing condition appropriately. This paper describes the implementation of a Godunov-type finite volume scheme based on unstructured adaptive grids for simulating flows on the meso-, micro- and urban-scales. The Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver used to calculate the Godunov fluxes is described in detail. The higher-order spatial accuracy is achieved via gradient reconstruction techniques after van Leer and the total variation diminishing condition is enforced with the aid of slope-limiters. A multi-stage explicit Runge-Kutta time marching scheme is used for maintaining higher-order accuracy in time. The scheme is conservative and exhibits minimal numerical dispersion and diffusion. The subgrid scale diffusion in the model is parameterized via the Smagorinsky-Lilly turbulence closure. The scheme uses a non-staggered mesh arrangement of variables (all quantities are cell-centered) and requires no explicit filtering for stability. A comparison with exact solutions shows that the scheme can resolve the different types of wave structures admitted by the atmospheric flow equation set. A qualitative evaluation for an idealized test case of convection in a neutral atmosphere is also presented. The scheme was able to simulate the onset of Kelvin-Helmholtz type instability and shows promise in simulating atmospheric flows characterized by sharp gradients without using explicit filtering for numerical stability.     

Well-balanced numerical modelling of non-uniform sediment transport in alluvial rivers

The last two decades have witnessed the development and application of well-balanced numerical models for shallow flows in natural rivers.However,until now there have been no such models for flows with non-uniform sediment transport.This paper presents a 1D well-balanced model to simulate flows and non-capacity transport of non-uniform sediment in alluvial rivers.The active layer formulation is adopted to resolve the change of bed sediment composition.In the framework of the finite volume Slope Llmiter Centred(SLIC) scheme,a surface gradient method is incorporated to attain well-balanced solutions to the governing equations.The proposed model is tested against typical cases with irregular topography,including the refilling of dredged trenches,aggradation due to sediment overloading and flood flow due to landslide dam failure.The agreement between the computed results and measured data is encouraging.Compared to a non-well-balanced model,the well-balanced model features improved performance in reproducing stage,velocity and bed deformation.It should find general applications for non-uniform sediment transport modelling in alluvial rivers,especially in mountain areas where the bed topography is mostly irregular.     

2-D NUMERICAL MODEL FOR FLOOD FORECAST IN RIVERS WITH HEAVILY SEDIMENT LADEN FLOW

I.INTRODUCTIONTwo-dimensionalnumericalmodelisaPOwerfoltoolforengineersandriVermanagerstopredictfloodhydxaulics,identifyareasofinundation,anddesignoptionsforfloodcontrollingstructures.SomespecialproblemswithheavilysedimentladenflowriVershouldbecarefullyconsideredforthenumericalmodeldesigning;1.theplaneformofariVerisusuallybraidedanditsmainchannelshiftsoften.Themainchannelandbarreplaceeachotherseveraltimesinonefloodevent.Atagivenlocationthewaterdepthmaychangefromover10meterstoseveralcenhm…     

DEPTH-AVERAGED 2-D CALCULATION OF TIDAL FLOW,SALINITY AND COHESIVE SEDIMENT TRANSPORT IN ESTUARIES

A depth-averaged 2-D numerical model for unsteady flow, salinity and cohesive sediment transport in estuaries is established using the finite volume method on the non-staggered, curvilinear grid. The convection terms are discretized by upwind schemes, the diffusion terms are by the central difference scheme, and the time derivative terms are by the three-time-level implicit scheme. The coupling of flow velocity and water level in the 2-D shallow water equations is achieved by the SIMPLEC algorithm with the Rhie and Chow's momentum interpolation method. The sediment model calculates the settling, deposition, erosion and transport of cohesive sediment, taking into account the influence of sediment size, sediment concentration, salinity and turbulence intensity on the flocculation of cohesive sediment. The flow model is first tested against the measurement data in the Tokyo Bay and San Francisco Bay, showing good agreements. And then, the entire model of flow, salinity and sediment transport is verified in the Gironde Estuary. The water elevation, flow velocity, salinity and sediment concentration are well predicted.     

A mathematical model for unsteady supercritical flow on a mobile sandy bed

ABSTRACT

Supercritical flow with sediment transport is a common phenomenon in steep rivers. This kind of flow presents features not present in rivers flowing in subcritical conditions. The development of a mathematical model to simulate supercritical flow with sediment transport in sandy rivers is described. The model is based on a numerical scheme for the integral version of the full governing equations and takes into account bottom configurations.     

Use of Large-Eddy Simulation for the bed shear stress estimation over a dune

Environmental flows are generally characterized by complex bed morphology and high current speeds. Such configurations favor the formation of vortex structures that strongly affect hydrody-namics and sediment transport. Large-Eddy Simulation (LES) enables investigation of the dynam-ics of the largest turbulence scales and, thanks to enhanced calculation resources, has now become applicable for simulating environmental flows. In this paper, a LES approach is developed in a CFD code (TELEMAC-3D), which was originally developed to simulate free surface flows using RANS methods. The present developments involve implementing subgrid models, boundary con-ditions and numerical schemes suitable for LES. The LES version of TELEMAC-3D was validated by comparing results on the model with experimental data for flow past a cylinder. Then, the model was applied to a test case representing flow over dunes. After validating the hydrodynamics, the model was used to assess the bottom shear stress, using both a RANS and a LES approach. Com-parison highlighted the potential contribution of LES to investigating the hydrodynamic forces acting on the bottom.     

Simulation of submerged granular flows by development of a two-phase incompressible explicit mesh-free method

The interaction between fluid and sediment particles is widely involved in hydraulic engineering problems. In the current study, an explicit incompressible mesh-free method in the framework of the Moving Particle Semi-implicit(MPS) method is proposed to simulate the interaction between the two phases in submerged conditions. The proposed method solves two sets of the continuity and momentum equations, respectively, for the fluid phase and the sediment phase according to the mixture theory. In th...     

Simulation of dam-break waves on movable beds using a multi-stage centered scheme

This paper presents the application of the multi-stage first-order centered scheme GMUSTA to solve a two-phase flow model with four equations for simulating dam-break floods without and with sediment transport.Computation of generalized Riemann invariants can be particularly complex and costly in simulating dam-break floods with sediment transport.GMUSTA numerical scheme,which does not require complete knowledge of the eigenstructure of the hyperbolic mathematical model,offers a suitable and attractive option.The quality of the dam-break flood simulations with GMUSTA scheme is verified by comparing the results against laboratory tests and some experimental data available in the literature,on fixed and mobile bed conditions,with different bed materials and flush or stepped bottoms.The numerical results reproduce quite well the experimental evidence,proving that the model is capable of predicting the temporal evolution of the free-surface and the bed.The GMUSTA scheme,which is not only simple to implement but also both accurate and computationally efficient,is proposed as an appropriate tool for integrating non-equilibrium sediment-transport models.     

Two-phase hydrodynamic and sediment transport modeling of wave-generated sheet flow

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–ε$k''–''\epsilon$ 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.     

One-dimensional numerical simulation of non-uniform sediment transport under unsteady flows

One-dimensional numerical models are popularly used in sediment transport research because they can be easily programmed and cost less time compared with two- and three-dimensional numerical models. In particular, they possess greater capacity to be applied in large river basins with many tributaries. This paper presents a one-dimensional numerical model capable of calculating total-load sediment transport. The cross-section-averaged sediment transport capacity and recovery coefficient are addressed in the suspended load model. This one-dimensional model, therefore, can be applied to fine suspended loads and to hyperconcentrated flows in the Yellow River. Moreover, a new discretization scheme for the equation of unsteady non-uniform suspended sediment transport is proposed. The model is calibrated using data measured from the Yantan Reservoir on the Hongshui River and the Sanmenxia Reservoir on the Yellow River. A comparison of the calculated water level and river bed deformation with field measurements Shows that the improved numerical model is capable of predicting flow, sediment transport, bed changes, and bed-material sorting in various situations, with reasonable accuracy and reliability.     

Shallow sediment transport flow computation using time-varying sediment adaptation length

Based on the common approach,the adaptation length in sediment transport is normally estimated astemporally independent.However,this approach might not be theoretically justified as the process of reaching the sediment transport equilibrium stage is affected by the flow conditions in time,especially for fast moving flows,such as scour-hole developing flows.In this study,the two-dimensional（2D） shallow water formulation together with a sediment continuity-concentration（SCC） model were applied to flow with mobile sediment boundary.A timevarying approach was proposed to determine the sediment transport adaptation length to simulate the sediment erosion-deposition rate.The proposed computational model was based on the Finite Volume（FV） method.The Monotone Upwind Scheme of Conservative Laws（MUSCL）-Hancock scheme was used with the Harten Lax van Leer-contact（HLLC） approximate Riemann solver to discretize the FV model.In the flow applications of this paper,a highly discontinuous dam-break,fast sediment transport flow was used to calibrate the proposed timevarying sediment adaptation length model.Then the calibrated model was further applied to two separate experimental sediment transport flow applications documented in the literature,i.e.a highly concentrated sediment transport flow in a wide alluvial channel and a sediment aggradation flow.Good agreement with the experimental data were obtained with the proposed model simulations.The tests prove that the proposed model,which was calibrated by the discontinuous dam-break bed scouring flow,also performed well to represent rapid bed change and steady sediment mobility conditions.     

Simulation of dam-break flow with grid adaptation

The unsteady free surface flow caused by sudden collapse of a dam produces discontinuities in the flow variables. As the flow surges downstream, it forms a moving bore front with steep gradients of water height and velocity. In the numerical simulation of this flow, proper grid distribution can play a crucial part in the prediction and resolution of the solutions. The use of presently available numerical schemes to solve this problem on a uniform course grid system fails to resolve the characteristic flow features and hence do a poor job in simulating this flow. In this paper, an adaptive grid which adjusts itself as the solution evolves is used for a better resolution of the flow properties. Rai and Anderson's¹² method is used to determine the grid speed; however, a different partial differential equation based on the conservative principle of grid arc lengths for clustering grids in one-dimensional flow is used along with the St. Venant equations to numerically simulate the flow. Both the subcritical and the supercritical flows under extreme boundary conditions are solved using this technique. With a specified number of grid points, this provides better quality solutions as compared to those obtained with uniformly distributed grids.     

One-dimensional morphodynamic model for retrogressive erosion based on a sediment entrainment theory at high flow velocity

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.