Two-Dimensional Depth-Averaged Flow Modeling with an Unstructured Hybrid Mesh

An unstructured hybrid mesh numerical method is developed to simulate open channel flows. The method is applicable to arbitrarily shaped mesh cells and offers a framework to unify many mesh topologies into a single formulation. A finite-volume discretization is applied to the two-dimensional depth-averaged equations such that mass conservation is satisfied both locally and globally. An automatic wetting-drying procedure is incorporated in conjunction with a segregated solution procedure that chooses the water surface elevation as the main variable. The method is applicable to both steady and unsteady flows and covers the entire flow range: subcritical, transcritical, and supercritical. The proposed numerical method is well suited to natural river flows with a combination of main channels, side channels, bars, floodplains, and in-stream structures. Technical details of the method are presented, verification studies are performed using a number of simple flows, and a practical natural river is modeled to illustrate issues of calibration and validation.     

Upland Erosion Modeling in a Semihumid Environment via the Water Erosion Prediction Project Model

The major water quality impairment in the midwest United States is sediment eroded from agricultural lands. Yet, few understand the spatial and temporal variability of erosion, or soil erosion dynamics, in relation to precipitation, topography, land management, and severe events. The objectives of this paper are to (1) develop a methodology for estimating long-term spatial soil erosion and water runoff losses and (2) explore issues in applying an established physical-based process model, Water Erosion Prediction Project (WEPP), to a large area by establishing a prototype system for the state of Iowa. This study for the first time provides a comparison of the model predictions against long-term measurements of the sediment delivery ratio (SDR) in the South Amana Catchment of the Clear Creek Watershed (CCW), a heavily instrumented watershed that is roughly 10 times the maximum WEPP fold size. To further examine the performance of WEPP in a semihumid environment, such as the CCW, where runoff and raindrop impact to erosion may be significant, the SDR was plotted as a function of the runoff coefficient, defined as the runoff/rainfall ratio. In addition, the WEPP predictions are compared against the statistical relation of SDR vs. runoff coefficient developed by Piest et al. in 1975) for watersheds in Iowa. It is shown that WEPP follows the trend shown by Piest et al. quite closely and performs well for continuous simulations extended up to 300?years.     

Investigation on the Suitability of Two-Dimensional Depth-Averaged Models for Bend-Flow Simulation

A numerical experiment is carried out to study the suitability of two-dimensional (2D) depth-averaged modeling for bend-flow simulation, in which the geometry of the studied channel is rectangular. Two commonly used 2D depth-averaged models for bend-flow simulation are considered in this study of which the bend-flow model includes the dispersion stress terms by incorporating the assumption of secondary-current velocity profile, and the conventional model neglects the dispersion stress terms. The maximum relative discrepancy of the longitudinal velocity, obtained from the comparison of these two models, is used as a criterion to judge their applicability for bend-flow simulation. The analysis of simulation results indicated that the maximum relative difference in longitudinal velocity is mainly related to the relative strength of the secondary current and the relative length of the channel. Empirical relations between the maximum relative difference in the longitudinal velocity, the relative strength of the secondary current, and the relative length of the channel for both the channel-bend region and the straight region following the bend have been established. The proposed relations provide a guideline for model users to determine the proper approach to simulate the bend-flow problem by either using the conventional model or the bend-flow model. Experimental data have been adopted herein to demonstrate the applicability and to verify the accuracy of the proposed relations.     

Limitations of Depth-Averaged Modeling for Shallow Wakes

Large-scale horizontal vortical structures are generic features of shallow flows which are often modeled using the two-dimensional (2D) depth-averaged equations. Such modeling is investigated for the well-defined case of shallow wakes of a conical island of small side slope for which a three-dimensional (3D) boundary-layer (3DBL) model has previously been validated through comparison with experiment. The 3DBL model used a 3D, two-mixing-length, eddy-viscosity turbulence model with a vertical mixing length of classical Prandtl form and a horizontal mixing length some multiple of this. A multiple of six gave good predictions. This mixing length approach is reduced to depth-averaged form, giving a horizontal mixing length of about half the water depth. The shallow wakes may be vortex shedding or steady/stable and are conventionally defined by a stability parameter. The critical value above which a stable wake is formed is considerably overestimated by the depth-averaged model (for a range of mixing lengths) and the length of stable wake bubble is considerably underestimated. It seems likely that this is because the amplification of friction coefficient due to horizontal strain rates is not represented. However, when vortex shedding is prominent the 2D and 3DBL wake structures are quite similar. These results show, for example, the limitations of depth-averaged models for the prediction of solute dispersion.     

Two-Dimensional Total Sediment Load Model Equations

An unsteady total load equation is derived for use in depth-averaged sediment transport models. The equation does not require the load to be segregated a priori into bed and suspended but rather automatically switches to suspended load, bed load, or mixed load depending on a transport mode parameter consisting of local flow hydraulics. Further, the sediment transport velocity, developed from available data, is explicitly tracked, and makes the equation suitable for unsteady events of sediment movement. The equation can be applied to multiple size fractions and ensures smooth transition of sediment variables between bed load and suspended load for each size fraction. The new contributions of the current work are the consistent treatment of sediment concentration in the model equation and the empirical definition of parameters that ensure smooth transitions of sediment variables between suspended load and bed load.     

Depth-Averaged Two-Dimensional Numerical Modeling of Unsteady Flow and Nonuniform Sediment Transport in Open Channels

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.     

Modeling Two-Dimensional Infiltration from Irrigation Furrows

Numerical simulation of the two-dimensional (2D) infiltration process during furrow irrigation requires considerable computational effort, which can be reduced by analytical modeling. This paper deals with the further development of the semianalytical infiltration model FURINF (furrow infiltration). Considering the varying impact of gravity and furrow geometry, the new approach models the impact of furrow geometry on infiltration progress using a transient geometric shape factor as a function of infiltration time and furrow geometry. FURINF portrays 2D infiltration from the wetted furrow perimeter by a series of one-dimensional (1D) infiltration computations that are performed in this paper on the basis of an analytical as well as a numerical solution of the 1D Richards equation. Comparing the FURINF results provided by the analytical and numerical 1D infiltration model confirmed the adequacy and reliability of the robust and simple analytical approach, which only requires soil parameters provided by rather simple measurements. The results and performances of the analytical FURINF model (FURINF-A) are compared within the frame of a sensitivity and error analysis with the outcome of the numerical subsurface flow model HYDRUS-2D considering three different soils.     

Integrated Two-Dimensional Surface and Three-Dimensional Subsurface Contaminant Transport Model Considering Soil Erosion and Sorption

To investigate the complex hydrological, morphodynamic, and environmental processes in watersheds, a physically-based integrated two-dimensional (2D) surface and three-dimensional (3D) subsurface model for flow, soil erosion and transport, and contaminant transport in the surface-subsurface system is presented in this paper. The model simulates the rainfall-induced surface flow by solving the depth-averaged 2D diffusion wave equation and the variably-saturated subsurface flow by solving the 3D mixed-form Richards equation. The surface and subsurface flow equations are coupled using the continuity conditions of pressure and exchange flux at the ground surface. The model uses the concept of nonequilibrium in the depth-averaged 2D simulation of nonuniform total-load sediment transport in upland fields, considering detachments by rainsplash and hydraulic erosion driven by surface flow. The integrated 2D surface and 3D subsurface contaminant transport model takes into account the contaminant changes due to sediment sorption and desorption, as well as exchanges between surface and subsurface domains due to infiltration, diffusion, and bed change. The model applies the same set of surface equations of flow, sediment, and contaminant transport for describing both upland areas and streams, so that no special treatments are required at their interface. The established model has been evaluated by comparisons with published experimental, numerical, and analytical data and then applied in an agricultural watershed. The model is suitable for wetland areas and agricultural watersheds in which streams are not very narrow and deep, and meanwhile a relatively fine mesh that can distinguish the streams is preferred.     

Two-Dimensional Fast-Response Flood Modeling: Desktop Parallel Computing and Domain Tracking

Emergency flood management is enhanced by using models that can estimate the timing and location of flooding. Typically, flood routing and inundation prediction is accomplished by using one-dimensional (1D) models. These have been the models of choice because they are computationally simple and quick. However, these models do not adequately represent the complex physical processes present for shallow flows located in the floodplain or in urban areas. Two-dimensional (2D) models developed on the basis of the full hydrodynamic equations can be used to represent the complex flow phenomena that exist in the floodplain and are, therefore, recommended by the National Research Council for increased use in flood analysis studies. The major limitation of these models is the increased computational cost. Two-dimensional flood models are prime candidates for parallel computing, but traditional methods/equipment (e.g., message passing paradigm) are more complex in terms of code refactoring and hardware setup. In addition, these hardware systems may not be available or accessible to modelers conducting flood analyses. This paper presents a 2D flood model that implements multithreading for use on now-prevalent multicore computers. This desktop parallel computing architecture has been shown to decrease computation time by 14 times on a 16-processor computer and, when coupled with a wet cell tracking algorithm, has been shown to decrease computation by as much as 310 times. These accomplishments make high-fidelity flood modeling more feasible for flood inundation studies using readily available desktop computers.     

Erosion of Finite Thickness Sediment Beds by Single and Multiple Circular Jets

Sediment management in reservoirs with the help of water jets has motivated this work. Erosion caused by single and multiple submerged circular turbulent wall jets on a noncohesive sediment bed of finite thickness lying on a fixed boundary was studied with the help of laboratory experiments. Different combinations of jet diameter, jet separation, and sediment thickness to jet diameter ratio were tested. Results show a relation between dimensionless parameters characterizing the steady state bed profile and the densimetric particle Froude number F0 given by the velocity at the nozzle and the effective diameter and submerged specific density of the sediment. Evolution of scour with time confirms previous studies where the erosion was found to initially grow with the logarithm of time up to a certain reference time t*. This time, made dimensionless with a time scale tc involving the volume of sediment scoured and the rate of erosion, was also related to the densimetric Froude number. A comparison with studies regarding erosion of a semiinfinite layer of sediment is also presented.     

Two-Dimensional Nonequilibrium Noncohesive and Cohesive Sediment Transport Model

The purpose of this paper is to develop an unsteady 2D depth-averaged model for nonuniform sediment transport in alluvial channels. In this model, the orthogonal curvilinear coordinate system is adopted; the transport mechanisms of cohesive and noncohesive sediment are both embedded; the suspended load and bed load are treated separately. In addition, the processes of hydraulic sorting, armoring, and bed consolidation are also included in the model. The implicit two-step split-operator approach is used to solve the flow governing equations and the coupling approach with iterative method are used to solve the mass-conservation equation of suspended sediment, mass-conservation equation of active-layer sediment, and global mass-conservation equation for bed sediment simultaneously. Three sets of data, including suspension transport, degradation and aggradation cases for noncohesive sediment, and aggradation, degradation, and consolidation cases for cohesive sediment, have been demonstrated to show the rationality and accuracy of the model. Finally, the model is applied to evaluate the desilting efficiency for Ah Gong Diann Reservoir located in Taiwan to show its applicability.     

Three-Dimensional and Depth-Averaged Large-Eddy Simulations of Some Shallow Water Flows

Three-dimensional (3D) and two-dimensional (2D) depth-averaged (DA) large-eddy simulations (LES) are presented for three different shallow-water flows involving large-scale horizontal structures: a mixing layer, the flow around a circular cylinder, and the flow in a groyne field. The results are compared with each other and also with experiments. In the 3D-LES, most of the energy-containing turbulent motions, including the larger subdepth-scale motions, are resolved, while in the 2D-DA-LES the effect of the 3D subdepth-scale turbulence is represented by a quadratic bottom-friction model and a simple eddy-viscosity model. In the case of the mixing layer, an additional stochastic backscatter model is necessary to account for the energy transfer from the subdepth-scale turbulence to the 2D structures in order to generate the latter. The 3D-LES results are generally in good agreement with the experiments, including the evolution of the horizontal structures. The much more economic 2D-DA-LES are somewhat less realistic in detail but also produce results that are generally of sufficient accuracy for practical purposes.     

Investigation of the Importance of Spatial Resolution for Two-Dimensional Shallow-Water Model Accuracy

The importance of spatial resolution for two-dimensional shallow-water model accuracy has been investigated by testing the effect of mesh refinement on two test cases based on laboratory dam-break experiments. A balanced first-order accurate upwind Q-Scheme and a second-order accurate upwind Hancock Monotone Upstream-centered Scheme for Conservation Laws scheme were both first validated on an analytical test, and then applied to the experimental dam-break test cases on four meshes of different density. Simulation results were evaluated through comparison of experimental and computed water level values at several available gauge points. Model sensitivity analysis showed that (1) mesh density was not critical for results accuracy; (2) excessive mesh refinement somewhat deteriorated the results; and (3) optimal spatial resolution was relatively low. Response is shown to be highly complex and no simple relation between spatial resolution and model accuracy has been found.     

Simulation of Airfoil Icing with a Novel Morphogenetic Model

In this paper, we describe a new modeling approach to tackle the challenging problem of in-flight icing prediction. In this approach, termed morphogenetic modeling, we predict the structural details of aircraft ice accretion by emulating the behavior of individual fluid elements. A two-dimensional morphogenetic model is used here to predict the ice accretion shape forming on a National Advisory Committee For Aeronautics 0012 airfoil under various atmospheric conditions. The influence of the surface heat transfer formulation on the ice accretion shape is examined. We complement the numerical simulation with an analytical model for airfoil icing that is based on a simple form of the mass and heat conservation equations. This analytical investigation allows us to identify a significant new dimensionless ratio, the runback factor, defined as the ratio of the impinging water mass flux to the freezing mass flux at the stagnation line. An increasing runback factor leads to a quantifiable downstream displacement of the accretion mass. We also use the analytical model to verify the morphogenetic model during the early stages of icing, and find that there is reasonable agreement between the two models in terms of ice accretion shape. A comparison with experimental data and other models shows that even simple morphogenetic modeling is competitive with existing models. Further improvements will take advantage of the model’s unique ability to simulate discontinuous ice accretions in complex geometries, leading to a considerable advancement in the simulation of in-flight icing.     

Full Two-Dimensional Model for Rolling Resistance. II: Viscoelastic Cylinders on Rigid Ground

Following the previous paper, “Full two-dimensional model for rolling resistance: Hard cylinder on viscoelastic foundation of finite thickness,” addressing modeling of rigid cylinder rolling against viscoelastic foundation of finite thickness, this paper focuses on the development of a rigorous full two-dimensional semianalytical model for viscoelastic rollers with layered structure rolling against a rigid ground. In this model, the polar coordinate system is used, the solution is expanded into a set of Fourier series corresponding to the angular coordinate, the frequency domain master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special condensed structure model based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. Examples are given to show the model capabilities to efficiently handle rolling resistance and contact stresses, and capture major characteristics of standing-wave phenomenon, such as sharp rise of rolling resistance, emergence of standing waves and material dynamic softening as the rolling speed approaches a critical value. The methodology may be of interest to industrial roller designers.     

Modeling In-Sewer Deposit Erosion to Predict Sewer Flow Quality

High levels of suspended solids are typically observed during the initial part of storms. Field evidence suggests that these suspended solids derive from the erosion of in-sewer sediment beds accumulated during dry and previous wet weather periods. Suspended sediment transport rate models within existing sewer network modeling tools have utilized inappropriate transport rate relationships developed mainly in fluvial environments. A process model that can account for the erosion of fine-grained highly organic in-sewer sediment deposits has been formulated. Values of parameters describing the increase in deposit strength with depth are required. These values are obtained using a genetic algorithm based calibration routine that ensures model simulations of suspended sediment concentrations that correspond to field data collected in a discrete length of sewer in Paris under known hydraulic event conditions. These results demonstrate the applicability of this modeling approach in simulating the magnitude and temporal distribution of suspended in-sewer sediment eroded by time varying flow. Further work is developing techniques to enable the application of this type of model at the network level.     

Two-Dimensional Simulation Model for Contour Basin Layouts in Southeast Australia. I: Rectangular Basins

Contour basin irrigation layouts are used to irrigate rice and other cereal crops on heavy cracking soils in Southeast Australia. In this study, a physically based two-dimensional simulation model that incorporates all the features of contour basin irrigation systems is developed. The model’s governing equations are based on a zero-inertia approximation to the two-dimensional shallow water equations of motion. The equations of motion are transformed into a single nonlinear advection–diffusion equation in which the friction force is described by Manning’s formula. The empirical Kostiakov equation and the quasi-analytical Parlange equation are used to model the infiltration process. The governing equations are solved by using a split-operator approach. The numerical procedure described here is capable of modeling rectangular basins; a procedure for irregular shaped basins is presented in Paper II. The model was validated against field data collected on commercial lasered contour layouts.     

Modeling Depth-Averaged Velocity and Boundary Shear in Trapezoidal Channels with Secondary Flows

The Shiono and Knight method (SKM) offers a new approach to calculating the lateral distributions of depth-averaged velocity and boundary shear stress for flows in straight prismatic channels. It accounts for bed shear, lateral shear, and secondary flow effects via 3 coefficients—f,λ, and Γ—thus incorporating some key 3D flow feature into a lateral distribution model for streamwise motion. The SKM incorporates the effects of secondary flows by specifying an appropriate value for the Γ parameter depending on the sense of direction of the secondary flows, commensurate with the derivative of the term Hρ(UV)d. The values of the transverse velocities, V, have been shown to be consistent with observation. A wide range of boundary shear stress data for trapezoidal channels from different sources has been used to validate the model. The accuracy of the predictions is good, despite the simplicity of the model, although some calibration problems remain. The SKM thus offers an alternative methodology to the more traditional computational fluid dynamics (CFD) approach, giving velocities and boundary shear stress for practical problems, but at much less computational effort than CFD.     

Two-Dimensional Simulation Model for Contour Basin Layouts in Southeast Australia. II: Irregular Shape and Multiple Basins

The development of a two-dimensional simulation model for single regular shape (rectangular) contour basin irrigation layout in southeast Australia is reported in a companion paper. Contour basin layouts as used in Southeast Australia are often irregular in shape and laid out as multiple basin systems. Irrigation of these basins is carried out sequentially involving back flow to the supply channel and inter-basin flow. This paper presents the extension of the earlier model to incorporate irregular shape basins and multiple basin operation. The governing equation is solved by adopting a “split-operator approach” using the method of characteristics coupled with two-dimensional Taylor series expansion for interpolation and calculation of diffusion terms. The numerical solution scheme is based on a grid of quadrilaterals for spatial discretization, to provide geometric flexibility. Infiltration is computed using either the empirical Kostiakov–Lewis equation or the quasianalytical Parlange equation. The model was validated against field data collected from irrigation events monitored on a commercial laser leveled contour layout consisting of five basins.