Venant Model Research Articles

Simulation of 2D Depth Averaged Saint Venant Model of Shatt Al Arab River South of Iraq

Simulation of 2D Depth Averaged Saint Venant Model of Shatt Al Arab River South of Iraq

Closed-form expressions of shear deformability tensors associated with a new beam model

The application of a recent beam model requires the evaluation of a suitably defined shear deformability tensor in order to ensure both energetic and geometric consistency with the 3D Saint Venant model subjected to non-uniform flexure and torsion. Actually, whatever is the position of the shearing force, the beam model provides the same elastic energy and the same tip displacement of the barycentric axis of the 3D Saint Venant model. The expression of the shear deformability tensor is rather involved since it depends upon three harmonic functions, namely the warping and the warpage functions associated, respectively, with torsion and shear. For this reason, in order to promote its use and shed some light on its properties, we derive explicit expressions of the shear deformability tensor for circular, elliptical and rectangular sections exploiting the relevant analytical formulas of the warping and warpage functions.

Estimation of multiple inflows and effective channel by assimilation of multi-satellite hydraulic signatures: The ungauged anabranching Negro river

With the upcoming SWOT satellite mission, which should provide spatially dense river surface elevation, width and slope observations globally, comes the opportunity to assimilate such data into hydrodynamic models, from the reach scale to the hydrographic network scale. Based on the HiVDI (Hierarchical Variational Discharge Inversion) modeling strategy (Larnier et al. (2020)), this study tackles the forward and inverse modeling capabilities of distributed channel parameters and multiple inflows (in the 1D Saint–Venant model) from multisatellite observations of river surface. It is shown on synthetic cases that the estimation of both inflows and distributed channel parameters (bathymetry-friction) is achievable with a minimum spatial observability between inflows as long as their hydraulic signature is sampled. Next, a real case is studied: 871km of the Negro river (Amazon basin) including complex multichannel reaches, 21 tributaries and backwater controls from major confluences. An effective modeling approach is proposed using (i) WS elevations from ENVISAT data and dense in situ GPS flow lines (Moreira (2016)), (ii) average river top widths from optical imagery (Pekel et al. (2016)), (iii) upstream and lateral flows from the MGB large-scale hydrological model (Paiva et al. (2013a)). The calibrated effective hydraulic model closely fits satellite altimetry observations and presents real-like spatial variabilities; flood wave propagation and water surface observation frequential features are analyzed with identifiability maps following (Brisset et al. (2018)). Synthetic SWOT observations are generated from the simulated flowlines and allow to infer model parameters (436 effective bathymetry points, 17 friction patches and 22 upstream and lateral hydrographs) given hydraulically coherent prior parameter values. Inferences of channel parameters carried out on this fine hydraulic model applied at a large scale give satisfying results using noisy SWOT-like data at reach scale. Inferences of spatially distributed temporal parameters (lateral inflows) give satisfying results as well, with even relatively small scale hydrograph variations being inferred accurately on this long reach. This study brings insights in: (i) the hydraulic visibility of the signatures of multiple inflow hydrographs at a large scale with SWOT; (ii) the simultaneous identifiability of spatially distributed channel parameters and inflows by assimilation of satellite altimetry data; (iii) the need for prior information; (iv) the need to further tailor and scale network hydrodynamic models and assimilation methods to improve the fusion of multisource information and potential information feedback to hydrological modules in integrated chains.

On the assimilation of altimetric data in 1D Saint–Venant river flow models

Abstract Given altimetry measurements, the identification capability of time varying inflow discharge Qin(t) and the Strickler coefficient K (defined as a power-law in h the water depth) of the 1D river Saint–Venant model is investigated. Various altimetry satellite missions provide water level elevation measurements of wide rivers, in particular the future Surface Water and Ocean Topography (SWOT) mission. An original and synthetic reading of all the available information (data, wave propagation and the Manning-Strickler’s law residual) are represented on the so-called identifiability map. The latter provides in the space-time plane a comprehensive overview of the inverse problem features. Inferences based on Variational Data Assimilation (VDA) are investigated at the limit of the data-model inversion capability : relatively short river portions, relatively infrequent observations, that is inverse problems presenting a low identifiability index. The inflow discharge Qin(t) is inferred simultaneously with the varying coefficient K(h). The bed level is either given or inferred from a lower complexity model. The experiments and analysis are conducted for different scenarios (SWOT-like or multi-sensors-like). The scenarios differ by the observation frequency and by the identifiability index. Sensitivity analyses with respect to the observation errors and to the first guess values demonstrate the robustness of the VDA inferences. Finally this study aiming at fusing relatively sparse altimetric data and the 1D Saint–Venant river flow model highlights the spatiotemporal resolution lower limit, also the great potential in terms of discharge inference including for a single river reach.

Global stability of weak solutions for a multilayer Saint–Venant model with interactions between layers

This paper concerns the global stability of weak solutions for the multilayer system introduced by Audusse et al., which models incompressible free surface flows. To do this, it is proven that this model admits the so called BD-entropy and a gain of integrability on the velocity. It allows to obtain enough compactness estimates in order to show the stability of global weak solutions.

Design and Application of an Adaptive Time Delay Model for Flow Routing in Prismatic Trapezoidal Geometry River Reach

Simplified flow routing model is favourably used for control-based application because it does not only present acceptable results but also is computationally inexpensive. Recently, the Time Delay model (TD) with two parameters, time constant and time delay has been developed in order to approximate the river flow in a very wide rectangular profile. This paper presents an advancement we thereafter call Adaptive Time Delay model (ATD) that expands the application scope of the TD Model by simulating the flow using a prismatic trapezoidal geometry. Firstly, the mathematical representation of the ATD model and the linearized Saint Venant model (SVE) are defined. Secondly, the transfer functions of the ATD model and the complex hydraulic model (SVE) are obtained by Laplace transformation. Finally, the Taylor expansion technique is used to find cumulants of the two transfer functions, and consequently equating the cumulants to derive time constant and time delay of the ATD model as functions of the complex hydraulic model parameters. By applying the fourth order Runge Kutta numerical scheme the flow rate and water level at downstream reach end are simulated. The innovation of this research is that both water stage and flow rate are derived through optimization. The performance of the ATD Model is also presented and compared to the TD Model in a case study. The extension of the time delay model does not only issue more accurate results but also introduces more outcomes like flow rate, and relation curves between time delay and time constant with discharge that might be useful in flood forecasting and other purposes in water resources operation.

Study on nonlinear damage creep constitutive model for high-stress soft rock

Rock engineering especially deep rock engineering undergoing long-term effects of external loading and gravity all or most may gradually damage deformation or creep deformation accumulation, leading rock structures to damage, crack, such as severe plastic deformation or even progressive failure. In this paper, based on the nonlinear damage creep characteristics of rock and damage variable, a new nonlinear damage creep constitutive model of high-stress soft rock is defined in series with the improved Burgers model, Hooke model and St. Venant model. This new nonlinear damage creep constitutive model can work out fairly reasonably explanations for the soft rock creep deformation. A series of uniaxial compression creep tests were performed to study the creep damage characteristics of typical soft rock in Jinchuan No.2 Mine in the northwest of China. Using the increment step loading and single-step loading, the results of creep experiments and nonlinear damage creep constitutive model results are very consistent in this study. The new model not only can reflect the whole course of creep deformation, but also can reasonably describe the soft rock under different initial creep stage, steady-state creep stage and accelerated creep stage. Therefore, the new nonlinear creep damage model is a reasonable reference model for the research of soft rock creep.

Realistic rendering for physically based shallow water simulation in Virtual Geographic Environments (VGEs)

Physically based realistic simulations enhance our understanding of complex environmental systems. In this paper, we analyse human perceptions of shallow water phenomena and present a set of physically based methods to visualize the dynamics of shallow water. A graphical processing units-based computing framework is shown to facilitate interactive visualization. The Saint–Venant model is adopted to describe shallow water dynamics. High-frequency waves are reconstructed from the flow directions to enrich the high-frequency waves for coarsely scaled georeferenced grids and to provide a better representation of the underlying flow field. The light-transport model is derived based on a simplified radioactive transfer process in which the scattering and absorption of water can be parameterized to reflect the optical behaviours of various water constituents. The experiments demonstrate that the proposed visualization methods can provide enhanced realism for physically based shallow water simulation.

Model based control for run-of-river system. Part 1: Model implementation and tuning

Optimal operation and control of a run-of-river hydro power plant depends on good knowledge of the elements of the plant in the form of models. River reaches are often considered shallow channels with free surfaces. A typical model for such reaches use the Saint Venant model, which is a 1D distributed model based on the mass and momentum balances. This combination of free surface and momentum balance makes the problem numerically challenging to solve. The finite volume method with staggered grid was compared with the Kurganov-Petrova central upwind scheme, and was used to illustrate the dynamics of the river upstream from the Gronvollfoss run-of-river power plant in Telemark, Norway, operated by Skagerak Energi AS. In an experiment on the Gronvollfoss run-of-river power plant, a step was injected in the upstream inlet flow at Arlifoss, and the resulting change in level in front of the dam at the Gronvollfoss plant was logged. The results from the theoretical Saint Venant model was then compared to the experimental results. Because of uncertainties in the geometry of the river reach (river bed slope, etc.), the slope and length of the varying slope parts were tuned manually to improve the fit. Then, friction factor, river width and height drop of the river was tuned by minimizing a least squares criterion. The results of the improved model (numerically, tuned to experiments), is a model that can be further used for control synthesis and analysis.

Simulation of Initiation, Transport, and Deposition of Granular Avalanches: Current Progress and Future Challenges

Since 1989 models to route debris flows and avalanches for hazards mitigation have been constructed using the seminal work of Savage and Hutter. With this approach a Saint Venant model for wet or dry granular flow is constructed by depth integrating equations for mass and momentum conservation, evaluating stress using bulk mixture values and a Coulomb failure criterion. Such models rely on just three forces to determine whether motion will occur: the force giving downslope acceleration, drag along the bed during flow, and the stress gradients derived from variations in thickness of the flow. With this construction most avalanche models simply begin with a force imbalance set large enough to reproduce the runout and deposits observed. However research into granular flow mechanics has advanced our knowledge considerably in recent years, allowing construction of a new and more powerful class of models that incorporate the effects of changes in internal structure in the flow, and explicitly include phenomenon such as fluid-solid coupling during rapid deformation of saturated granular mixtures. The defining feature of these more sophisticated models is that they can evolve from a stable stress state into an unstable state such that, given certain conditions, an initially stable rock or soil masscanbegin to creep or deform slowly well before it eventually accelerates rapidly andflows downhill. The contrast between simple and sophisticated models is illustrated by comparison of a simple model for an estimated rockfall hazard in California using a Savage and Hutter approach with a sophisticated, fully coupled fluid-solid model that successfully simulated initiationand transport of experimental debris flows without arbitrarily adjusting any model parameters.

Impact of river bed morphology on discharge and water levels simulated by a 1D Saint–Venant hydraulic model at regional scale

Summary River cross-sections data are required to represent channel geometry in hydrodynamic models. In the absence of accurate data at regional scale, simplified or parameterized cross sections are often used, which might affect the performance of the hydrodynamic model. In this study we assess the sensitivity of a 1D Saint–Venant hydraulic model to different types of river morphological data. The question is addressed using a 1D unsteady hydraulic model (HEC-RAS), with lateral inflows provided by the hydro(geo)logical model Eau-Dyssee, to explore a wide spectrum of river geometry scenarios, regarding river bed slopes and cross-sectional shapes. The target scale is the one of the Seine River (France). As a gateway for larger and more complex regional hydro(geo)logical applications, our case-study covers a well-described 89-km reach in a sub-tributary of the Seine River. River morphology is described by high-resolution cross-sections, and Manning’s roughness coefficient ( n ) is used for calibration against observed discharges and river stages in a mid-reach control point, with satisfactory performances over the 8-year simulation period. The resulting model still simulates realistic discharge hydrographs when forced with degraded channel geometry data, using either fewer cross-sections or approximated ones. In such cases, however, the hydraulic model does not always satisfactorily predict the associated water levels when compared to observations. In certain geometry scenarios, the RMSE between simulated water levels using degraded geometry and observations may go up to 0.3 m. The study confirms that the accuracy of predicted water levels and maximum water depths simulated by a Saint–Venant model relies on an accurate representation of channel geometry and bed level slopes along the river reach. From the various scenarios, it appears that the longitudinal description of the bed level profiles has a larger impact on the simulation of water levels than the cross-sectional shapes. This offers interesting implications for flood forecast mapping applications and regional scale models that often use simplified river geometry and Digital Elevation Models (DEMs) built by remote sensing technologies to simulate the water levels.

One Dimensional Numerical Simulation of Bed Changes in Irrigation Channels using Finite Volume Method

A one-dimensional Saint Venant model is developed using the Einstein sediment transport formula for simulating hydraulics and bed changes in irrigation channels . The governing equations are discretized using Finite Volume Method. The Central-Upwind method is used in this study to calculate the numerical flux. The model gives a stable and good prediction of sub, super and transcritical flows and captures harp changes such as hydraulic jump without leading to numerical oscillation or diffusion. An experimental test case is adopted to examine the performance of this mode. The simulated results show a good agreement with experimental data in the upstream section, and can predict an average value of measured profile in the downstream section of a steep channel. The knick point movement is successfully predicted by the model. The model appears to be a potential and reasonably accurate tool to predict bed changes in irrigation channels due to the water flow.

A remark on free boundary problem of 1-D compressible Navier-Stokes equations with density-dependent viscosity

In this paper, we prove the existence and uniqueness of the weak solution of the one-dimensional compressible Navier–Stokes equations with density-dependent viscosity µ(ρ)=ρθ with θ∈(0, γ⊲2], γ>1. The initial data are a perturbation of a corresponding steady solution and continuously contact with vacuum on the free boundary. The obtained results apply for the one-dimensional Siant–Venant model of shallow water and generalize ones in (Arch. Rational Mech. Anal. 2006; 182: 223–253). Copyright © 2009 John Wiley & Sons, Ltd.

A quasi-secant continuous model for the analysis of long-span cable-stayed bridges

In this paper a non-linear continuous model for the statical analysis of long-span cable-stayed bridges with fan scheme and H-shaped towers is proposed. This model is based on a quasi-secant large-displacement formulation of the stays-deck interaction and involves an Euler-Bernoulli/De Saint Venant model for the girder. An approximate closed-form solution of the statical problem, in which flexural and torsional terms are coupled, is obtained by means of a perturbative technique and according to the prevailing “truss-like” structural behavior. Results for some study-cases are compared with those relevant to both classical models and numerical solutions, proving effectiveness and applicability of the proposed model.

Spherically Symmetric Isentropic Compressible Flows with Density-Dependent Viscosity Coefficients

We prove the existence of global weak solutions to the compressible Navier–Stokes equations with density-dependent viscosity coefficients when the initial data are large and spherically symmetric by constructing suitable aproximate solutions. We focus on the case where those coefficients vanish on vacuum. The solutions are obtained as limits of solutions in annular regions between two balls, and the equations hold in the sense of distribution in the entire space-time domain. In particular, we prove the existence of spherically symmetric solutions to the Saint–Venant model for shallow water.

Application of a second‐order Runge–Kutta discontinuous Galerkin scheme for the shallow water equations with source terms

AbstractThe present work addresses the numerical prediction of discontinuous shallow water flows by the application of a second‐order Runge–Kutta discontinuous Galerkin scheme (RKDG2). The unsteady flow of water in a one‐dimensional approach is described by the Saint Venant's model which incorporates source terms in practical applications. Therefore, the RKDG2 scheme is reformulated with a simple way to integrate source terms. Further, an adequate boundary conditions handling, by the theory of characteristics, was overviewed to be adapted to the external points of the mesh, as well as to some points of local invalidity of the Saint Venant's model. To validate the proposed technique, steady and transient test problems (all having a reference solution) were considered and computed by means of the overall method. The results were illustrated jointly with the reference solution and the results carried out by a traditional second‐order finite volume (FV2) scheme implemented with the same techniques as the RKDG2. The proposed method has proven its practical consideration when solving discontinuous shallow water flow involving: non‐prismatic channels, various cross‐sections, smoothly varying bed topography and internal boundary conditions. Copyright © 2007 John Wiley & Sons, Ltd.

A Saint Venant model for gravity driven shallow water flows with variable density and compressibility effects

We introduce a new model for shallow water flows with non-flat bottom made of two layers of compressible–incompressible fluids. The classical Savage–Hutter model for gravity driven shallow water flows is derived from incompressible Euler equations. Here, we generalize this model by adding an upper compressible layer. We obtain a model of shallow water type, that admits an entropy dissipation inequality, preserves the steady state of a lake at rest and gives an approximation of the free surface compressible–incompressible Euler equations.

Complementary aspects of linear flood routing modelling and flood frequency analysis

AbstractSimilarity and differences between linear flood routing modelling (LFRM) and flood frequency analysis (FFA) techniques are presented. The moment matching used in LFRM to approximate the impulse response function (IRF) was applied in FFA to derive the asymptotic bias caused by the false distribution assumption. Proceeding in this way, other estimation methods were used as approximation methods in FFA to derive the asymptotic bias. Using simulation experiments, the above investigation was extended to evaluate the sampling bias. As a feedback, the maximum likelihood method (MLM) can be used for approximating linear channel response (LCR) by the IRFs of conceptual models.Impulse responses of the convective diffusion and kinematic diffusion models were applied and developed as FFA models. Based on kinematic diffusion LFRM, the equivalence of estimation problems of discrete‐continuous distribution and single‐censored sample are shown both for the method of moments (MOM) and the MLM. Hence, the applicability of MOM is extended for the case of censored samples.Owing to the complexity and non‐linearity of hydrological systems and resulting processes, the use of simple models is often questionable. The rationale of simple models is discussed. The problems of model choice and overparameterization are common in mathematical modelling and FF modelling. Some results for the use of simple models in the stationary FFA are presented. The problems of model discrimination are then discussed.Finally, a conjunction of linear stochastic processes and LFRM is presented. The influence of river courses on stochastic properties of the runoff process is shown by combining Gaussian input with the LCR of the simplified Saint Venant model. It is shown that, from the classification of the ways of their development, both LFRM and FFA can benefit. Copyright © 2006 John Wiley & Sons, Ltd.

Two-dimensional depth-averaged modeling of flow in curved open channels

The application of the depth-averaged De St. Venant equations for open channel numerical models dictate the adoption of hydrostatic pressure distribution. They are thus applicable to cases where vertical details are not significant. The alternative two-dimensional vertically averaged and moment equations model, in which more vertical details are accounted for, is used to analyze problems involved in curved channels of various curvature. The distribution of horizontal velocity components is assumed to be linear, while the vertical velocity and pressure is quadratic. The implicit Petrov-Galerkin finite element scheme is used in these simulations. Computed values for water surface profile, depth-averaged longitudinal and transverse velocities across the channel width and vertical profiles of longitudinal and transverse velocities are compared with experimental data. The comparison shows a good agreement between the simulated results and experimental data. In addition, this study recommends the supplement of the standard conventional De St. Venant model by the proposed model on simulating strongly curved flows. Finally, the use of refined finite element meshes is recommended only when some of the details near the channel edges are sought.

Numerical modeling of avalanches based on Saint Venant equations using a kinetic scheme

Numerical modeling of debris avalanche is presented here. The model uses the long‐wave approximation based on the small aspect ratio of debris avalanches as in classical Saint Venant model of shallow water. Depth‐averaged equations using this approximation are derived in a reference frame linked to the topography. Debris avalanche is treated here as a single‐phase, dry granular flow with Coulomb‐type behavior. The numerical finite volume method uses a kinetic scheme based on the description of the microscopic behavior of the system to define numerical fluxes at the interfaces of a finite element mesh. The main advantage of this method is to preserve the height positivity. The originality of the presented scheme stands in the introduction of a Dirac distribution of particles at the microscopic scale in order to describe the stopping of a granular mass when the driving forces are under the Coulomb threshold. Comparisons with analytical solutions for dam break problems and experimental results show the efficiency of the model in dealing with significant discontinuities and reproducing the flowing and stopping phase of granular avalanches. The ability of the model to describe debris avalanche behavior is illustrated here by schematic numerical simulation of an avalanche over simplified topography. Coulomb‐type behavior with constant and variable friction angle is compared in the framework of this simple example. Numerical tests show that such an approach not only provides insights into the flowing and stopping stage of the granular mass but allows observation of interesting behavior such as the existence of a fluid‐like zone behind a stopped solid‐like granular mass in specific situations, suggesting the presence of horizontal surfaces in the deposited mass.