INVERSE FLOOD WAVE ROUTING USING SAINT VENANT EQUATIONS

A numerical model for routing of flood wave in a part of meandering river is presented. It is based on a modified form of the complete one-dimensional Saint-Venant equations of unsteady flow. These equations were modified such that flows in the meandering river channel, left over bank flood plain, and right over bank flood plain were all identified separately. Thus, the differences in hydraulic and geometric properties and flow-path distances were considered for all three divisions of the valley cross-section. This development differs from conventional one-dimensional treatment of unsteady flows in rivers with flood plain wherein the flow is either averaged across the total cross-sectional area (channel and flood plain) or the flood plain is treated as off-channel storage, and the reach lengths of the channel and flood plain are assumed to be identical. The weighted four-point implicit finite difference method is selected to solve a modified Sain-Venant equations for its versatility and computing efficiency. The numerical model was applied to the Euphrates river at the reach between Haditha dam and Hit city along (124.4 km) to make a sensitivity analysis of the following parameters: maximum flood wave discharge, maximum flood wave elevation, lag time of the peak discharge, lag time of the peak level, and time of arrival of flood wave to a seven major cities along the Euphrates river in a case study and comparing it with a same parameters produced when a conventional one-dimensional treatment of unsteady flows in river with flood plains where the meandering in river is neglected.

Journal of Applied Engineering Sciences, 2020

This research concerns about the development and application of Variable Parameter Kinematic Wave Numerical model (VPKWM) based on 1-D Saint-Venant equation, to study the behaviour of the propagation of a flood wave in Non-prismatic natural waterways in an ungauged basin. The channel slope and wetted perimeter are considered as variable because of the irregularity of the boundary of the channel and the change in magnitude of discharge. The scarcity of reliable inflow data at upstream is a serious problem for the flood routing process in an ungauged basin. In this study the inflow hydrograph and lateral inflow hydrographs are obtained using SCS-CN method as rainfall runoff model. The performance of the model assessed considering four parameters such as root mean square error (RMSE), peak discharge, peak time and total volume. The results indicated that the VPKWM for non-prismatic channel provided reasonable output compared with the observed data.

waterjournal.cn

Flooding is a common natural disaster that causes enormous economic, social, and human losses. Of various flood routing methods, the dynamic wave model is one of the best approaches for the prediction of the characteristics of floods during their propagations in natural rivers because all of the terms of the momentum equation are considered in the model. However, no significant research has been conducted on how the model sensitivity affects the accuracy of the downstream hydrograph. In this study, a comprehensive analysis of the input parameters of the dynamic wave model was performed through field applications in natural rivers and routing experiments in artificial channels using the graphical multi-parametric sensitivity analysis (GMPSA). The results indicate that the effects of input parameter errors on the output results are more significant in special situations, such as lower values of Manning's roughness coefficient and/or a steeper bed slope on the characteristics of a design hydrograph, larger values of the skewness factor and/or time to peak on the channel characteristics, larger values of Manning's roughness coefficient and/or the bed slope on the space step, and lower values of Manning's roughness coefficient and/or a steeper bed slope on the time step and weighting factor.

Flood Routing is a mathematical procedure for predicting the changing magnitude, Speed and shape of a flood wave as a function of time at one or more points along a Watercourse. When a flood wave moves downstream a river, the wave configuration will be modified due to channel irregularities and roughness. Flood routing is important in the design of flood protection measures, to estimate how the proposed measures will affect the behavior of flood waves in rivers, so that adequate protection and economic solutions may be found. Flood routing procedures may be classified as either hydrological or hydraulics. Hydrological methods use the principle of continuity and a relationship between discharge and the temporary storage of excess volumes of water during the flood period. Hydraulic methods of routing involve the numerical solutions of the convective diffusion equations, the one dimensional Saint Venant equations of gradually varied unsteady flow in open channels. In present research, the examination of the several hydraulic, hydrologic methods, have been proceeded for several rivers data, compared with a written hand program in MATLAB software analysis. Also, a comparison was made between the results of various methods, using statistical analysis for river data employed. Furthermore, several hydraulic methods are compared through a series of numerical experiments that covered varied channel bed slopes, varied roughness coefficient and varied unsteady flow with different hydrograph geometric shapes. The results indicated that the developed methods generally provided reasonable output compared with the observed measured hydrologic data provided.

A numerical model for routing of flood wave in a part of meandering river is presented. It is based on a modified form of the complete one-dimensional Saint-Venant equations of unsteady flow. These equations were modified such that flows in the meandering river channel, left over bank flood plain, and right over bank flood plain were all identified separately. Thus, the differences in hydraulic and geometric properties and flow-path distances were considered for all three divisions of the valley cross-section. This development differs from conventional one-dimensional treatment of unsteady flows in rivers with flood plain wherein the flow is either averaged across the total cross-sectional area (channel and flood plain) or the flood plain is treated as off-channel storage, and the reach lengths of the channel and flood plain are assumed to be identical. The weighted four-point implicit finite difference method is selected to solve a modified Sain-Venant equations for its versatility and computing efficiency. The numerical model was applied to the Euphrates river at the reach between Haditha dam and Hit city along (124.4 km) to make a sensitivity analysis of the following parameters: maximum flood wave discharge, maximum flood wave elevation, lag time of the peak discharge, lag time of the peak level, and time of arrival of flood wave to a seven major cities along the Euphrates river in a case study and comparing it with a same parameters produced when a conventional one-dimensional treatment of unsteady flows in river with flood plains where the meandering in river is neglected.

River flow predictions are needed in many water resources management. The beginning of the modern study of unsteady flow in open channels can be traced to the latter half of the nineteenth century when the French engineer Saint-Venant introduced the partial differential equations of continuity and momentum governing free surface flow in open channels. These equations are highly nonlinear and therefore do not have analytical solutions. The computer revolution in twentieth century made a new era where numeric methods can be utilized effectively to solve nonlinear partial differential equations. This paper presents the results of two different numerical methods, namely; Preissmann and Lax diffusive schemes for numerical solution of Saint-Venant equations that govern the propagation of flood wave, in natural rivers, with the objective of the better understanding of this propagation process. The results have shown that the hydraulic parameters play important game in the flood wave propagation. The results of these numerical solutions are compared with the HEC-RAS commercial computer model.

Journal of Hydrology, 1996

The Salnt-Venant equations are used to describe river waves. Generally, for flood muting in rivers, the Saint-Venant system is reduced to the diffusive wave equation which can be resolved using finite-difference algorithms. The choice of a numerical method, and of the space and time steps to be retained, depends essentially on the form of flood hydrographs and the hydraulic properties of the river. This paper investigates these areas; two sets of criteria are proposed, the first to define parameter ranges representing each wave type and then, in the particular case of the diffusive wave model, to define criteria for the choice of numerical algorithm and appropriate space and time steps. The first analysis was based on the concept that river wave behaviour is determined by the balance between friction and inertia. The conclusions relate to the magnitude of temporal character° istics of flood waves, expressed as a function of the Froude number of the steady uniform flow and a dimensionless wave number of the unsteady component of the motion. The second part discussed questions related to the diffusive wave problem and to numerical instabilities. A technique is proposed to guide the user in the choice of the computational algorithm and specifies the error introduced by numerical methods. The technique was applied to flood-roaring simulation for the Loire river in France. In this case, two finite-difference algorithm~ were compared to the exact solution given by the analytical method. Comparisons between results show the efficiency of the technique to optimise the choice of the finite-dif:ference method and the adequate space and time steps.

Flood routing was studied here has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. Floods were taken unsteady flows that vary by time and location. Equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional the Saint-Venant hypothesis were considered. Dynamic wave model as one of the flood routing methods was examined for flooding operations because of its high accuracy. The best numerical methods and various schemes was the main challenge for optimal modeling of dynamic waves and predicting flooding behavior. A 78-km reach of Ghare-Aghaj River hydrometric Station was investigated and hyperbolic nonlinear partial differential equations were solved. Preissmann Implicit Scheme and Mac-Cormak Explicit Scheme were modeled using finite difference numerical methods. Developed models were also compared to one of the most reliable Mike series computer program. It was aimed to find the most suitable numerical finite difference scheme based on computing skills and coding output results. The results confirmed the superiority of Preissmann Implicit Scheme in predicting flood wave characteristics for the studied area.

Water Resources Development and Management, 2019

Flood forecasting based on the distributed model is becoming popular in Malaysia. It is one of the methods to reduce flood risk when a structural measure is very expensive to implement. Two main outputs from the forecasting model are the timing of the flood wave to arrive in the area of interest and the magnitude of the flood. However, another factor, which needs to be given attention, is the simulation computational time. Flood forecasting model demands a fast and accurate computation. The river channel is normally represented by river cross-section that deployed the full hydrodynamic equation. But when come to modeling a reservoir, three common methods can be applied which are lumped flow routing using pool routing method, 1-Dimensional and 2-Dimensional dynamic wave routing. This paper discusses the significance of the different methods applied to represent the flood wave propagation in branching and nearly full reservoir. Beris Dam reservoir was selected for the analysis. Since no data available for calibration, the assessment is purely analytical. The results show that there are differences of time and magnitude for floodwater to start spilling from the spillway. The simulation time for the pool routing is very short as compared to 1D and 2D. Where this is making attractive for flood forecasting but there is a need in the future to apply the 2D method for a large reservoir.

2014

Flood wave propagation in river channel flow can be enunciated by nonlinear equations of motion for unsteady flow. It is difficult to find analytical solution of these non-linear equations. Hence, in this paper verification of the finite element model has been carried out against available numerical predictions and field data. The results of the model indicate a good matching with both Preissmann scheme and HEC-RAS model for a river reach of 29km at both sites (15km from upstream and at downstream end) for discharge hydrographs. It also has an agreeable comparison with the Preissemann scheme for the flow depth (stage) hydrographs. The proposed model has also been applying to forecast daily discharges at 400km downstream in the Indus River from Sukkur barrage of Sindh, Pakistan, which demonstrates accurate model predictions with observed the daily discharges. Hence, this model may be utilized for flood warnings in advance. Keywords— Finite Element Method, Flood Forecasting, HECRAS, I...