Upwind Conservative Scheme for the Saint Venant Equations

An upwind conservative scheme with a weighted average water-surface-gradient approach is proposed to compute one-dimensional open channel flows. The numerical scheme is based on the control volume method. The intercell flux is computed by the one-sided upwind method. The water surface gradient is evaluated by the weighted average of both upwind and downwind gradients. The scheme is tested with various examples, including dam-break problems in channels with rectangular and triangular cross-sections, hydraulic jump, partial dam-break problem, overtopping flow, a steady flow over bump with hydraulic jump, and a dam-break flood case in a natural river valley. Comparisons between numerical and exact solutions or experimental data demonstrated that the proposed scheme is capable of accurately reproducing various open channel flows, including subcritical, supercritical, and transcritical flows. The scheme is inherently robust, stable, and monotone. The scheme does not require any special treatment, such as artificial viscosity or front tracking technique, to capture steep gradients or discontinuities in the solution.     

Sediment Transport in River Models with Overbank Flows

Some laboratory sediment-transport experiments are described in which a compound channel with a mobile-bed composed of uniform sand with a d50 of 0.88?mm was subjected to overbank flows. The main river channel was monitored to determine the effect of floodplain roughness on conveyance capacity, bed-form geometry, resistance, bed-load transport, and dune migration rate. The floodplain roughness was varied to simulate a wide range of conditions, commensurate with conditions that can occur in a natural river. For a given discharge, the main river channel bed was found to adjust itself to a quasi-equilibrium condition governed by the lateral momentum transfer between the floodplain and main channel flows and the local alluvial resistance relationship appropriate for the proportion of total flow in the main river channel. The sediment transport rate was found to reflect all these influences. The data are summarized in equation form for comparison with other experimental studies and for checking numerical river simulation models.     

Simple, Robust, and Efficient Algorithm for Gradually Varied Subcritical Flow Simulation in General Channel Networks

This paper details the development of a method for subcritical flow modeling in channel networks by using the implicit finite-difference method. The method treats backwater effects at the junction points on the basis of junction-point water stage prediction and correction (JPWSPC). It is applicable to flows in both looped and nonlooped channel networks and has no requirement on the flow directions. The method is implemented in a numerical model, in which the Saint-Venant equations are discretized by using the four-point implicit Preissmann scheme, and the resulting nonlinear system of equations is solved by using the Newton-Raphson method. With the help of JPWSPC, each branch is computed independently. This guarantees the simplicity, efficiency, and robustness of the numerical model. The model is applied to two hypothetic channel networks and a real-life river network in South China. All the networks contain both branched and looped structures. The simulated results compare well with the results from literature or the measurements.     

Evaluation of Flow Resistance in Smooth Rectangular Open Channels with Modified Prandtl Friction Law

Flow resistance in open channels is usually estimated by applying the approach that is developed originally for pipe flows. Such estimates may be useful for engineering applications but always differ from measurements to some extent. This paper first summarizes empirical approaches that have been proposed in the literature to reconcile the resistance difference. These include various modifications of the pipe friction for applications to rectangular ducts and open channel flows. An improved friction equation is then derived for evaluating flow resistance of smooth rectangular open channels. Comparisons are made with experimental data reported by previous researchers and those collected in the present study. It is shown that the new proposed equation is applicable for both narrow and wide channels and is more accurate than those available in the literature.     

Flow and Velocity Distribution in Meandering Compound Channels

An investigation of flow and velocity distribution in meandering compound channels with over bank flow is described. Equations concerning the three-dimensional variation of longitudinal, transverse, and vertical velocity in the main channel and floodplain of compound section in terms of channel parameters are presented. The flow and velocity distributions in meandering compound channels are strongly governed by interaction between flow in the main channel and that in the floodplain. The proposed equations take adequate care of the interaction affect. Results from the formulations, simulating the three-dimensional velocity field in the main channel and in the floodplain of meandering compound channels are compared with their respective experimental channel data obtained from a series of symmetrical and unsymmetrical test channels with smooth and rough sections. The aspect ratio of the test channels varies from two to five. The equations are found to be in good agreement with the experimental data. The formulations are verified against the natural river and other meandering compound channel data. The power laws used for simulating the three-dimensional velocity structure are found to be quite adequate.     

Three-Dimensional Numerical Modeling of Initial Mixing of Thermal Discharges at Real-Life Configurations

A three-dimensional Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) model is developed for simulating initial mixing in the near field of thermal discharges at real-life geometrical configurations. The domain decomposition method with multilevel embedded overset grids is employed to handle the complexity of real-life diffusers as well as to efficiently account for the large disparity in length scales arising from the relative size of the ambient river reach and the typical diffuser diameter. An algebraic mixing length model with a Richardson-number correction for buoyancy effects is used for the turbulence closure. The governing equations are solved with a second-order-accurate, finite-volume, artificial compressibility method. The model is validated by applying it to simulate thermally stratified shear flows and negatively buoyant wall jet flows and the computed results are shown to be in good overall agreement with the experimental measurements. To demonstrate the potential of the numerical model as a powerful engineering simulation tool we apply it to simulate turbulent initial mixing of thermal discharges loaded from both single-port and multiport diffusers in a prismatic channel and a natural river. Comparisons of the CFD model results with those obtained by applying two widely used empirical mixing zone models show that the results are very similar in terms of both the rate of dilution and overall shape of the plumes. The CFD model further resolves the complex three-dimensional features of such flows, including the complex interplay of the ambient flow and thermal discharges as well as the interaction between each of discharges loaded from multiple ports, which are obviously not accessible by the simpler empirical models.     

Efficient Approximation of Unsteady Friction Weighting Functions

A simple method is presented for evaluating wall shear stresses from known flow histories in unsteady pipe flows. The method builds on previous work by Trikha, but has two important differences. One of these enables the method to be used with much larger integration time steps than are acceptable with Trikha’s method. The other, a general procedure for determining approximations to weighting functions, enables it to be used at indefinitely small times (high frequencies). The method is applicable to both laminar and turbulent flows.     

Lateral Depth-Averaged Velocity Distributions and Bed Shear in Rectangular Compound Channels

This paper presents a method to predict depth-averaged velocity and bed shear stress for overbank flows in straight rectangular two-stage channels. An analytical solution to the depth-integrated Navier–Stokes equation is presented that includes the effects of bed friction, lateral turbulence, and secondary flows. The Shiono and Knight method accounts for bed shear, lateral shear, and secondary flow effects via three coefficients, f, λ, and Γ, respectively. A novel boundary condition at the internal wall between the main channel and the adjoined floodplain is proposed and discussed along with other conventional boundary conditions. The analytical solution using the novel boundary condition gives good prediction of both lateral velocity distribution and bed shear stress when compared with experimental data for different aspect ratios.     

Numerical Analysis of River Channel Processes with Bank Erosion

This paper presents a numerical analysis of river channel processes with bank erosion. The model can be used for investigating both bed-deformation and bankline shifting in 2D plan form. The basic equations are used in a moving boundary fitted-coordinate system, and a new formulation of nonequilibrium sediment transport is introduced to reproduce the channel processes. The model was applied to examine the morphological behavior of experimental channels. Temporal changes in the plan form in a meandering channel can be classified into two patterns: meander developing and meander straightening. Comparison of the observed and calculated results indicates that the model is applicable to both channel changes under various hydraulic conditions. On the basis of the numerical findings, the paper clarifies the influence of hydraulic variables on the location of bank erosion and bed scouring. The model also was used to investigate the effect of alternate bars on bank erosion and to investigate the development of channel meandering from an initially straight channel.     

Conservative Scheme for Numerical Modeling of Flow in Natural Geometry

A numerical model is proposed to compute one-dimensional open channel flows in natural streams involving steep, nonrectangular, and nonprismatic channels and including subcritical, supercritical, and transcritical flows. The Saint-Venant equations, written in a conservative form, are solved by employing a predictor-corrector finite volume method. A recently proposed reformulation of the source terms related to the channel topography allows the mass and momentum fluxes to be precisely balanced. Conceptually and algorithmically simple, the present model requires neither the solution of the Riemann problem at each cell interface nor any special additional correction to capture discontinuities in the solution such as artificial viscosity or shock-capturing techniques. The resulting scheme has been extensively tested under steady and unsteady flow conditions by reproducing various open channel geometries, both ideal and real, with nonuniform grids and without any interpolation of topographic survey data. The proposed model provides a versatile, stable, and robust tool for simulating transcritical sections and conserving mass.     

Lagrangian Modeling of Weakly Nonlinear Nonhydrostatic Shallow Water Waves in Open Channels

A Lagrangian, nonhydrostatic, Boussinesq model for weakly nonlinear and weakly dispersive flow is presented. The model is an extension of the hydrostatic model—dynamic river model. The model uses a second-order, staggered grid, predictor-corrector scheme with a fractional step method for the computation of the nonhydrostatic pressure. Numerical results for solitary waves and undular bores are compared with Korteweg-de Vries analytical solutions and published numerical, laboratory, and theoretical results. The model reproduced well known features of solitary waves, such as wave speed, wave height, balance between nonlinear steepening and wave dispersion, nonlinear interactions, and phase shifting when waves interact. It is shown that the Lagrangian moving grid is dynamically adaptive in that it ensures a compression of the grid size under the wave to provide higher resolution in this region. Also the model successfully reproduced a train of undular waves (short waves) from a long wave such that the predicted amplitude of the leading wave in the train agreed well with published numerical and experimental results. For prismatic channels, the method has no numerical diffusion and it is demonstrated that a simple second-order scheme suffices to provide an efficient and economical solution for predicting nonhydrostatic shallow water flows.     

Crack Growth Prediction by Manifold Method

The prediction of crack growth is studied by the manifold method. The manifold method is a new numerical method proposed by Shi. This method provides a unified framework for solving problems dealing with both continuums and jointed materials. It can be considered as a generalized finite-element method and discontinuous deformation analysis. One of the most innovative features of the method is that it employs both a physical mesh and a mathematical mesh to formulate the physical problem. The physical mesh is dictated by the physical boundary of a problem, while the mathematical mesh is dictated by the computational consideration. These two meshes are interrelated through the application of weighting functions. In this study, a local mesh refinement and auto-remeshing schemes are proposed to extend the manifold method. The proposed model is first verified by comparing the numerical results with the benchmark solutions, and the results show satisfactory accuracy. The crack growth problems and the stress distributions are then investigated. The manifold method is proposed as an attractively new numerical technique for fracture mechanics analysis.     

Two-Dimensional Solution for Straight and Meandering Overbank Flows

This paper presents a practical method to predict depth-averaged velocity and shear stress for straight and meandering overbank flows. An analytical solution to the depth-integrated turbulent form of the Navier-Stokes equation is presented that includes lateral shear and secondary flows in addition to bed friction. The novelty of the present approach is not only its inclusion of the secondary flows in the formulation but also its applicability to straight and meandering channels. The analytical solution is applied to a number of channels, at model and field scales, and is also compared with other available methods such as that of Shiono and Knight and the lateral distribution method. The present formulation gives much better predictions of velocity and shear stress, particularly in those cases where the secondary flows are dominant.     

Three-Dimensional Hydrodynamics of Meandering Compound Channels

The velocity field in meandering compound channels with overbank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields using computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. In particular, an accurate computer prediction of the velocity field could benefit studies of channel morphology and pollution transport. In this paper, a meandering channel experiment from the U.K. Flood Channel Facility is simulated using computational fluid dynamics and the predicted velocities compared with the experimental data. Particular attention is paid to the reproduction of the secondary velocities and the helical motion of the water flowing within the main channel. Sensitivity tests of mesh design, discretization scheme, and roughness height are reported, together with the turbulence characteristics of the flow.     

Simulating Three-Dimensional Free Surface Viscoelastic Flows using Moving Finite Difference Schemes

An efficient finite difference framework based on moving meshes methods is developed for the three-dimensional free surface viscoelastic flows. The basic model equations are based on the incompressible Navier-Stokes equations and the Oldroyd-B constitutive model for viscoelastic flows is adopted. A logical domain semi-Lagrangian scheme is designed for moving-mesh solution interpolation and convection. Numerical results show that harmonic map based moving mesh methods can achieve better accuracy for viscoelastic flows with free boundaries while using much less memory and computational time compared to the uniform mesh simulations.     

Collection Conduits Including Subsurface Drains

Numerous types of pipes and channels with spatially increasing flows in environmental engineering applications are identified by type and function and referred to as collection conduits. An overview of methods for designing and analyzing collection conduits is provided. Full conduits with nonuniform and uniform inflow are first considered. Dimensional analysis is then employed to demonstrate the relationship between variables for open channels; that leads to the identification of possibilities for generalized numerical solutions. Prior collection conduit applications are discussed within the framework of the dimensional analysis (which also pertains to some constant-flow applications). A previously unpublished generalized numerical solution for rectangular collection conduits is presented. Subsurface drains are addressed with particular emphasis, including the use of numerical methods to develop a new generalized chart and relation to other design methods. Among the important conclusions for subsurface drains is that the somewhat common practice of using Manning’s equation alone for such problems is not generally adequate. Examples and practical design suggestions are included, and the use of computer-based numerical methods is discussed more generally.     

Analysis of Debris Wave Development with One-Dimensional Shallow-Water Equations

The objective of this contribution is to analyze the formation of debris waves in natural channels. Numerical simulations are carried out with a 1D code, based on shallow-water equations and on the weighted averaged flux method. The numerical code represents the incised channel geometry with a power-law relation between local width and flow depth and accounts for all source terms in the momentum equation. The debris mixture is treated as a homogeneous fluid over a fixed bottom, whose rheological behavior alternatively follows Herschel-Bulkley, Bingham, or generalized viscoplastic models. The code is first validated by applying it to dam-break tests on mudflows down a laboratory chute and verifying its efficiency in the simulation of rapid transients. Then, following the analytical method developed by Trowbridge, the stability of a uniform flow for a generalized viscoplastic fluid is examined, showing that debris flows become unstable for Froude numbers well below 1. Applications of the code to real debris flow events in the Cortina d’Ampezzo area (Dolomites) are presented and compared with available measured hydrographs. A statistical analysis of debris waves shows that a good representation of wave statistics can be obtained with a proper calibration of rheological parameters. Finally, it is shown that a minimum duration of debris event and channel length are required for waves showing up, and an explanation, confirmed both by field data and numerical simulations, is provided.     

Compatibility of Reservoir Sediment Flushing and River Protection

In this paper, we propose a system of numerical models for the compatibility assessment of reservoir sediment flushing and protection of downstream river environments. The model system is made up of two simulation models. The first model simulates soil erosion in watershed slopes and sediment transport in the tributary of the reservoir by means of a weighted essentially nonoscillatory (WENO) method, which is conservative and fourth-order accurate in space and time. The second model simulates velocity and suspended solid concentration fields in the reservoirs. This model is based on the three-dimensional (3D) numerical integration of motion and concentration equations, expressed in contravariant form on a generalized boundary-conforming curvilinear coordinate system by using a conservative and higher-order accurate numerical scheme. The proposed system of models is applied to the Pieve di Cadore (Veneto, Italy) reservoir and to its catchment area. By comparing suspended solid concentrations that are discharged through the bottom outlets during flushing operations with suspended solid concentrations in the main river during natural flooding, we perform an assessment of the compatibility between sediment flushing and the protection of the river ecosystem downstream.     

Three‐Dimensional Finite Element Analysis in Airport Pavement Design

This paper discusses work being performed at the Federal Aviation Administration (FAA) Airport Technology R&D Branch in the development of a three‐dimensional finite element‐based airport pavement design procedure for rigid airport pavements. The structure of the pavement design procedure and the function of the finite element structural model within it are described. A major focus of current FAA research and development efforts is on reducing run time. A simplified, single‐slab mesh runs on a personal computer and returns a maximum edge stress in a fraction of the time required by the full nine‐slab mesh. Results are presented for the simplified mesh for various aircraft types and slab sizes and compared to the larger mesh. Two types of foundation models are considered to represent a subgrade of infinite depth. A subgrade model consisting of discrete springs at nodal points approximates the distributed spring (Winkler) foundation with subgrade modulus k used in Westergaard analysis. An alternative model makes use of infinite elements to represent a linear elastic foundation with elastic modulus E and Poisson’s ratio μ. Stress computations using both models show that the Winkler foundation model is significantly more sensitive to slab size than the infinite element model for dual‐tridem (six‐wheel) aircraft gear loads. In a recent project at the FAA Center of Excellence (COE) for Airport Pavement Research, the open source code software (Nike3D) used in the three‐dimensional finite element computations to include the infinite element formulation. The infinite element was implemented as a new material type applicable to standard eight‐node elements in the Nike3D element library.     

Coupled and Decoupled Numerical Modeling of Flow and Morphological Evolution in Alluvial Rivers

Existing numerical river models are mostly built upon asynchronous solution of simplified governing equations. The strong coupling between water flow, sediment transport, and morphological evolution is thus ignored to a certain extent. An earlier study led to the development of a fully coupled model and identified the impacts of simplifications in the water-sediment mixture and global bed material continuity equations as well as of the asynchronous solution procedure for aggradation processes. This paper presents the results of an extended study along this line, highlighting the impacts on both aggradation and degradation processes. Simplifications in the continuity equations for the water-sediment mixture and bed material are found to have negligible effects on degradation. This is, however, in contrast to aggradation processes, in which the errors purely due to simplified continuity equations can be significant transiently. The asynchronous solution procedure is found to entail appreciable inaccuracy for both aggradation and degradation processes. Further, the asynchronous solution procedure can render the physical problem mathematically ill posed by invoking an extra upstream boundary condition in the supercritical flow regime. Finally, the impacts of simplified continuity equations and an asynchronous solution procedure are shown to be comparable with those of largely tuned friction factors, indicating their significance in calibrating numerical river models. It is concluded that the coupled system of complete governing equations needs to be synchronously solved for refined modeling of alluvial rivers.