Simplified Method for the Characterization of the Hydrograph following a Sudden Partial Dam Break

This paper presents a simplified approach to the characterization of the hydrograph following the partial collapse of concrete gravity dams. The proposed approach uses a simplified representation of the reservoir geometry and is based on the numerical solution of shallow water equations to study the two-dimensional evolution of the water surface within the reservoir. The numerical results are made dimensionless and reorganized so as to compute the peak discharge, the duration and the recession limb of the dam break hydrograph. The proposed practical approach provides a quite satisfactory reproduction of the computed hydrograph for a wide set of realistic situations that have been simulated in detail.     

Flood Simulation Using a Well-Balanced Shallow Flow Model

This work extends and improves a one-dimensional shallow flow model to two-dimensional (2D) for real-world flood simulations. The model solves a prebalanced formulation of the fully 2D shallow water equations, including friction source terms using a finite volume Godunov-type numerical scheme. A reconstruction method ensuring nonnegative depth is used along with a Harten, Lax, and van Leer approximate Riemann solver with the contact wave restored for calculation of interface fluxes. A local bed modification method is proposed to maintain the well-balanced property of the algorithm for simulations involving wetting and drying. Second-order accurate scheme is achieved by using the slope limited linear reconstruction together with a Runge-Kutta time integration method. The model is applicable to calculate different types of flood wave ranging from slow-varying inundations to extreme and violent floods, propagating over complex domains including natural terrains and dense urban areas. After validating against an analytical case of flow sloshing in a domain with a parabolic bed profile, the model is applied to simulate an inundation event in a 36?km2 floodplain in Thamesmead near London. The numerical predictions are compared with analytical solutions and alternative numerical results.     

Finite Volume Model for Two-Dimensional Shallow Environmental Flow

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.     

DORA Algorithm for Network Flow Models with Improved Stability and Convergence Properties

A new methodology for the solution of shallow water equations is applied for the computation of the unsteady-state flow in an urban drainage network. The inertial terms are neglected in the momentum equations and the solution is decoupled into one kinematic and one diffusive component. After a short presentation of the DORA (Double ORder Approximation) methodology in the case of a single open channel, the new methodology is applied to the case of a sewer network. The transition from partial to full section and vice versa is treated without the help of the Preissmann approximation. The algorithm also allows the computation of the diffusive component in the case of vertical topographic discontinuities, without the introduction of any internal boundary conditions and without any change in the structure of the linear system matrix. The algorithm is tested on one field example, and its performance is compared with the performance of other popular commercial codes.     

Design of Minimum Seepage Loss Canal Sections with Drainage Layer at Shallow Depth

This paper presents an analytical solution for the quantity of seepage from a rectangular canal underlain by a drainage layer at shallow depth. The solution has been obtained using inverse hodograph and conformal mapping. Using the solution for the rectangular canal and the existing analytical solutions for triangular and trapezoidal canals, simplified algebraic equations for computation of seepage loss from these canals, when the drainage layer lies at finite depth, have been presented, which replace the cumbersome evaluation of complex integrals. Using these seepage loss equations and a general uniform flow equation, simplified equations for the design variables of minimum seepage loss sections have been obtained for each of the three canal shapes by applying a nonlinear optimization technique. The optimal design equations along with the tabulated section shape coefficients provide a convenient method for design of the minimum seepage loss section. A step-by-step design procedure for rectangular and trapezoidal canal sections has been presented.     

Coupled 1D–Quasi-2D Flood Inundation Model with Unstructured Grids

A simplified numerical model for simulation of floodplain inundation resulting from naturally occurring floods in rivers is presented. Flow through the river is computed by solving the de Saint Venant equations with a one-dimensional (1D) finite volume approach. Spread of excess flood water spilling overbank from the river onto the floodplains is computed using a storage cell model discretized into an unstructured triangular grid. Flow exchange between the one-dimensional river cells and the adjacent floodplain cells or that between adjoining floodplain cells is represented by diffusive-wave approximated equation. A common problem related to the stability of such coupled models is discussed and a solution by way of linearization offered. The accuracy of the computed flow depths by the proposed model is estimated with respect to those predicted by a two-dimensional (2D) finite volume model on hypothetical river-floodplain domains. Finally, the predicted extent of inundation for a flood event on a stretch of River Severn, United Kingdom, by the model is compared to those of two proven two-dimensional flow simulation models and with observed imagery of the flood extents.     

SWAN-Mud: Engineering Model for Mud-Induced Wave Damping

This paper describes the implementation of a new dispersion relation and energy-dissipation equation obtained from a viscous two-layer model schematization in the state-of-the-art wave forecasting model SWAN to simulate wave damping in coastal areas by fluid mud deposits. This new dispersion relation is derived for a nonviscous, nonhydrostatic upper layer and a viscous, hydrostatic lower layer, covering most conditions encountered in nature. An algorithm is developed for a robust numerical solution of this new implicit dispersion relation through proper starting values in the iteration procedure. The implementation is tested against a series of analytical solutions and three schematic test cases. Next, four dispersion relations published in the literature are evaluated and compared with the new dispersion relation. The solution of the dispersion relations forms a multidimensional space. Comparison of the various model solutions through one-dimensional graphs can therefore become quite misleading, as shown in the discussion of a two-dimensional representation of the solution space, explaining for instance the variation in ambient conditions at which maximum wave damping is to be expected. The various models have been developed for a variety of conditions, such as shallow and deep water and shallow and thick mud layers; the various models agree well in their domain of applicability, but they show significant deviations when used outside their domain. Because the ambient and mud conditions may vary considerable in space and time at a particular site, the use of the new model is advocated because it covers most water depths and fluid mud thicknesses encountered in nature. The strength of the new SWAN-mud model lies in its large-scale applicability, assessing the two-dimensional evolution of wave fields in coastal areas. Therefore, the new implementation is evaluated with respect to the behavior of waves on a sloping seabed, representing real-world coasts. In all cases, the new SWAN-mud model behaves satisfactorily; a critical remaining issue, though, is the assessment of the relevant fluid mud parameters.     

Finite Volume Model for Nonlevel Basin Irrigation

A finite volume model for unsteady, two-dimensional, shallow water flow is developed and applied to simulate the advance and infiltration of an irrigation wave in two-dimensional basins of complex topography. The fluxes are computed with Roe's approximate Riemann solver and the monotone upstream scheme for conservation laws is used in conjunction with predictor-corrector time-stepping to provide a second-order accurate solution. Flux-limiting is implemented to eliminate spurious oscillations and the model incorporates an efficient and robust scheme to capture the wetting and drying of the soil. Model predictions are compared with experimental data for one- and two-dimensional problems involving rough, impermeable, and permeable beds, including a poorly leveled basin.     

Explicit Schemes for Dam-Break Simulations

Dam-break problems involve the formation of shocks and rarefaction fans. The performance of 20 explicit numerical schemes used to solve the shallow water wave equations for simulating the dam-break problem is examined. Results from these schemes have been compared with analytical solutions to the dam-break problem with finite water depth and dry bed downstream of the dam. Most of the numerical schemes produce reasonable results for subcritical flows. Their performance for problems where there is a transition between subcritical and supercritical flows is mixed. Although many numerical schemes satisfy the Rankine-Hugoniot condition, some produce solutions which do not satisfy the entropy condition, producing nonphysical solutions. This was the case for the majority of first-order schemes examined. Numerical schemes which consider critical flow in the solution are guaranteed to produce entropy satisfying solutions. Second-order schemes avoid the generation of expansive shocks; however, some form of flux or slope limiter must be used to eliminate oscillations that are associated with these schemes. These limiters increase the complexity and the computational effort required, but they are generally more accurate than their first-order counterparts. The limiters employed by these second-order schemes will produce monotone or total variation diminishing solutions for scalar equations. Some limiters do not exhibit these properties when they are applied to the nonlinear shallow water wave equations. This comparative study shows that there are a variety of shock-capturing numerical schemes that are efficient, accurate, robust, and are suitable for solving the shallow water wave equations when discontinuities are encountered in the problem.     

Numerical Solution of the Dam-Break Problem with a Discontinuous Galerkin Method

A discontinuous Galerkin method for the solution of the dam-break problem is presented. The scheme solves the shallow water equations with spectral elements, utilizing an efficient Roe approximate Riemann solver in order to capture bore waves. The solution is enhanced by a projection limiter that eliminates spurious oscillations near discontinuities. The main advantage of the model is the flexibility in approximating smooth solutions with high-order polynomials and resolving at the same time discontinuous shock waves. Furthermore, the finite element discretization is capable of handling complex geometries and producing correct results near the boundaries. Both the h- and p-type extensions are investigated for the one-dimensional dam break, and the results are verified by comparison with analytical solutions. The application to a two-dimensional dam-break problem shows the efficiency and stability of the method.     

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.     

Advances in Calculation Methods for Supercritical Flow in Spillway Channels

A calculation method is presented for applications to steady supercritical and transcritical flow in spillway channels. The method solves the two-dimensional nonlinear shallow water equations using a cell-centered finite-volume approach. High spatial resolution of shock waves and other steep flow features is achieved by employing MUSCL reconstruction and an approximate Riemann solver for the flux evaluations at each cell interface. The method can be implemented on boundary-conforming meshes to more accurately map the wide range of geometries that may occur in practice. Six analytical test problems are proposed for the validation of calculation methods applied to steady supercritical flow. These problems are used to validate the proposed flow solver, which is then applied to the case of steady supercritical flow in a curved channel transition, and comparisons are made with published data. Despite limitations in the shallow water model, the results show satisfactory agreement with data for the maximum rise in water level through the standing oblique shock waves.     

Two-Dimensional Analyses of Thermoplastic Culvert Deformations and Strains

Tests have been performed in a biaxial pipe test cell to develop baseline information on profiled pipe behavior under biaxial loading. These include a lined corrugated high-density polyethylene pipe and a helically wound ribbed polyvinyl chloride pipe. Results of the tests are utilized to examine the effectiveness of the two-dimensional methods of buried pipe analysis. Calculations of pipe responses by the two-dimensional finite element method and a set of simplified design equations are compared with the measurements of pipe strains and deflections. The study reveals that the two-dimensional finite element analysis can effectively be used to calculate pipe deflections and circumferential strains. The simplified equations appear suitable as design tools for standard buried thermoplastic pipe installations. Janbu’s nonlinear soil model with Mohr–Coulomb plasticity provided an effective simulation of the nonlinear soil behavior A study of pipes with low stiffness soil support under the haunches shows that this leads to strain concentrations in the pipe walls near that zone. Higher values of empirical strain factor, Df, are estimated to include this strain concentration during design.     

Finite-Element Modeling of Floodplain Flow

A new methodology for a robust solution of the diffusive shallow water equations is proposed. The methodology splits the unknowns of the momentum and continuity equations into one kinematic and one parabolic component. The kinematic component is solved using the slope of the water level surface computed in the previous time-step and a zero-order approximation of the water head inside the mass-balance area around each node of the mesh. The parabolic component is found by applying a standard finite-element Galerkin procedure, where the source terms can be computed from the solution of the previous kinematic problem. A simple 1D case, with a known analytical solution, is used to test the accuracy of the model. A second test is performed by comparing, in a more complex case, the flow rates computed by the model with the flow rates directly estimated from the computed water heads. An application to a real 2D case of flood flow on a river floodplain shows the practical advantages of the methodology.     

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.     

Brief Analysis of Shallow Water Equations Suitability to Numerically Simulate Supercritical Flow in Sharp Bends

This work deals with the suitability of two-dimensional shallow water equations for the numerical simulation of supercritical free surface flows in bends, when the usual hypothesis of small width/curvature radius ratio does not hold. Here, a very reliable and accurate finite-volume, Godunov-type scheme is adopted for the numerical integration of the governing equations. Comparison with a selected set of experimental laboratory data and asymptotic analytical solutions shows that several aspects concerning the physics of the phenomenon are well reproduced, such as the blocking of the stream when the Froude number of the undisturbed flow is not large enough and the bend is sufficiently sharp, while maximum water depth in the bend is systematically underestimated.     

Discontinuous Galerkin Finite-Element Method for Transcritical Two-Dimensional Shallow Water Flows

A total variation diminishing Runge Kutta discontinuous Galerkin finite-element method for two-dimensional depth-averaged shallow water equations has been developed. The scheme is well suited to handle complicated geometries and requires a simple treatment of boundary conditions and source terms to obtain high-order accuracy. The explicit time integration, together with the use of orthogonal shape functions, makes the method for the investigated flows computationally as efficient as comparable finite-volume schemes. For smooth parts of the solution, the scheme is second order for linear elements and third order for quadratic shape functions both in time and space. Shocks are usually captured within only two elements. Several steady transcritical and transient flows are investigated to confirm the accuracy and convergence of the scheme. The results show excellent agreement with analytical solutions. For investigating a flume experiment of supercritical open-channel flow, the method allows very good decoupling of the numerical and mathematical model, resulting in a nearly grid-independent solution. The simulation of an actual dam break shows the applicability of the scheme to nontrivial bathymetry and wave propagation on a dry bed.     

模拟降雨条件下南方某城市土壤中铀的迁移转化机制研究

土壤中放射性核素铀是主要天然辐射贡献者之一,当土壤中铀含量异常时其化学毒性和放射性会对人类健康产生严重威胁。城市是人口高密度区,明确土壤中铀含量水平是城市放射性地质调查重要工作,为城市规划区及潜在规划区提供基础数据支撑。以某城市土壤作为研究对象,通过静态吸附试验和模拟降雨动态淋滤试验方式,对城市放射性地质调查土壤中铀迁移转化机制进行分析研究。结果表明：加Cu离子使土壤铀吸附率下降9.7%;初始铀浓度、吸附时间、粒径大小表明定量土壤中吸附铀酰离子的负点电荷有限;pH为4~6的土壤吸附铀能力最强。SEM分析表明,吸附铀酰后,土壤表面由凹凸不平变为平滑、孔隙度减少及变小。铀在不同pH下的淋洗动力学均符合双常数动力学程,土壤表面对铀的释放表现为一定的微曲线性特征。在pH为4~6自然酸性条件下,当溶液中铀含量大于土壤时,土壤会吸附溶液中铀酰离子;当溶液中铀含量小于土壤时,土壤中铀酰离子易释放到溶液中。该研究为城市放射性地质调查提供了理论依据。     

Seepage from a Rectangular Ditch to the Groundwater Table

This study presents both a numerical and an experimental solution to seepage from a rectangular ditch or elongated pond to a groundwater table of infinite horizontal extent. Because of the unknown location of the free surface, the flow domain is transformed into the complex potential plane using the inverse formulation method, where the free surface becomes a straight line. The method of finite differences was used to solve the boundary value problem. The problem was also investigated experimentally using a sand tank model. For comparison purposes, a one-dimensional analytical solution is also presented. The results were compared with each other and with those available in the literature obtained with other solution techniques. The parameters affecting the seepage rate were investigated and the resulting relationships are presented in dimensionless graphs. It is believed that these graphs may be of use in design problems. The conditions for which the simplified one-dimensional analytical solution agrees well with the results of the sophisticated two-dimensional numerical solution are identified.