Numerical Simulation of Flood Routing using the Simplified Saint Venant Equations in Rectangular Channels

Floods, which cause a lot of damage, are a natural phenomenon that often occurs during the rainy season. Flood occurs because the discharge entering the channel exceeds the channel capacity. If the discharge data in the upstream area that will enter the channel is known, we can determine the flow behavior in the downstream area using a mathematical model. In this study, we proposed using simplified Saint Venant equations to simulate the flow routing in a prismatic channel with a rectangular section. This model is solved numerically using the finite difference method. Here, the numerical scheme used succeeds in simulating the flow behavior in the channel due to the discharge entering it. The simulation results show that the discharge entering the channel will propagate downstream with decreasing discharge quantity. Information on the amount of discharge at locations along the channel is useful as supporting data for flood control and prevention systems that will be conveyed to residents along the channel.Keywords: flood routing; prismatic channel; Saint Venant Equations; finite difference method. AbstrakBanjir yang menimbulkan banyak kerusakan merupakan fenomena alam yang sering terjadi pada musim hujan. Banjir terjadi karena debit yang masuk ke dalam kanal melebihi kapasitas kanalnya. Jika data debit di daerah hulu yang akan masuk ke dalam kanal diketahui, maka kita dapat menentukan perilaku aliran di daerah hilir dengan menggunakan model matematika. Dalam studi ini, kami mengusulkan untuk menggunakan persamaan Saint Venant yang disederhanakan untuk mensimulasikan penelusuran aliran pada saluran prismatik dengan penampang persegi panjang. Model ini diselesaikan secara numerik dengan menggunakan metode beda hingga. Di sini, skema numerik yang digunakan berhasil mensimulasikan perilaku aliran pada saluran akibat debit yang masuk. Hasil simulasi menunjukkan bahwa debit yang masuk ke saluran akan merambat ke hilir dengan kuantitas debit yang semakin berkurang. Informasi jumlah debit di lokasi sepanjang saluran ini berguna sebagai data pendukung pada sistem pengendalian dan pencegahan banjir yang akan disampaikan kepada penduduk di sepanjang kanal.Kata kunci: penelusuran banjir; saluran prismatik; persamaan Saint Venant; metode beda hingga.

The Translatory Wave Model for Landslides

The Saint-Venant equations are usually the basis of numerical models for landslide flows. They are nonstationary and nonlinear. The theory for translatory waves in a prismatic channel and a funneling channel can be used for landslides using the assumption of either turbulent or laminar flow in the slide. The mathematics of translatory waves traveling over dry land or superimposed on another flow are developed. This results in a new slope factor controlling the flow velocity, together with the Chezy coefficient used in previous applications of the translatory wave theory. Flow times for the slide to reach a given destination, slide depth, and velocity can be calculated using the initial magnitude of the flow in the slide. The instabilities of the wave tail are discussed. Three case studies are presented: a submarine slide that started the Tohoku tsunami in Japan, the Morsárjökull rock avalanche in SE Iceland, and the Móafellshyrna slide in central N Iceland.

1D flow simulation with irregular cross-sections using the pre-balanced shallow water equations

<p>With the possible climate change and increased pace of urbanization in the century, urban flooding has caused more and more attentions nowadays. Shallow water equations are widely used to reproduce the flow hydrodynamics of flooding around the urban areas, which have been proved a powerful tool for flood risk assessment and evacuation management, like river flow or flowing at drainage networks with irregular cross-sections at 1D scale. Over the last two decades, Godunov-type schemes have became popular for its robustness treating complex flow phenomenons. When tacking complex topography in the framework of Godunov-type scheme, sourer term needs to be treated property to preserve steady state, that flux gradient and sourer term are balanced. Capart et al. (2003) reconstructed the momentum flux by considering the balance of hydrostatic pressure with the approximated water surface level, which has the ability to tackle the irregular and non-prismatic channel flow with complex topography. This approximation is exact for two cases: 1) rectangular and prismatic channel; 2) water surface is horizontal. However, for other cases, approximation is employed to achieve the hydrostatic equilibrium, which has reduced the accuracy of the numerical solution and increased the complexity for the model implementation. </p><p>In this work, we present a new well-balanced numerical scheme for simulating 1D frictional shallow water flow with irregular cross-sections over complex topography involving wetting and drying. The proposed scheme solves, in a finite volume Godunov-type framework, a set of pre-balanced shallow water equations derived by considering pressure balancing (Liang and Marche, 2009). HLL approximated Riemann solver is adopted for the flux calculation at the cell interface. Non-negative reconstruction of Riemann state (Audusse et al., 2004) and local bed modification (Liang, 2010) produce stable and well-balanced solutions to shallow water flow hydrodynamics. Bed slope source term can be approximated using central difference and no special treatment is needed for wet and dry bed. The friction source term is discretized using a splitting implicit scheme and limiting value of friction force is used to ensure stability for the dry bottom (Liang and Marche, 2009). The new numerical scheme is validated against two theoretical benchmark tests and then compared with the validated shallow water model with circular and trapezoid cross-sections over complex topography involving wetting and drying. This method is also possible to reproduce the mixed flow in the conduit or for the flow with non-prismatic channel like river flow in the near future.</p><p>References</p><p>Audusse, E., Bouchut, F., Bristeau, M. O., Klein, R., & Perthame, B. T. (2004). A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM Journal on Scientific Computing, 25(6), 2050-2065.</p><p>Capart, H, Eldho, TI, Huang, SY, Young, DL, and Zech, Yves, "Treatment of natural geometry in finite volume river flow computations", Journal of Hydraulic Engineering 129, 5 (2003), pp. 385--393.</p><p>Liang, Qiuhua and Marche, Fabien, "Numerical resolution of well-balanced shallow water equations with complex source terms", Advances in water resources 32, 6 (2009), pp. 873--884.</p><p>Liang, Qiuhua, "Flood simulation using a well-balanced shallow flow model", Journal of hydraulic engineering 136, 9 (2010), pp. 669--675.</p>

Comparative Study of One Dimensional and Two Dimensional Steady Surface Flow Analysis

<p>Determination of actual water surface is required for design of hydraulic structures, reservoirs, flood plain management, and flood forecasting. Classical approach of analyzing the river flow using one dimensional flow analysis cannot provide the accurate information of water surface for different return period floods. So, both 1D and 2D steady surface flow analysis in prismatic channel and non-prismatic channel were done using models like HEC-RAS, FESWMS-2DH, GIS, and HECGEORAS to compare the results and recommended to select the best among these two flow analyses. Analysis of result showed that in prismatic channel, the water surface elevations obtained from 1D and 2D steady flow analysis for discharge Q=10cft/s were almost similar with maximum variation of 0.33ft. But in case of non-prismatic channel, the results of water surface elevations from 1D and 2D steady flow analysis for discharge Q = 5000cft/s and 9430cft/s were not similar and the maximum variation of 1.36ft and 1.75ft were found for two discharges respectively. 1D steady flow analysis is acceptable for prismatic channel except at bend which may require 2D analysis. But flow in non-prismatic channel requires 2D steady flow analysis for precise water surface elevation.</p><p><strong>Journal of Advanced College of Engineering and Management,</strong> Vol. 2, 2016, Page: 15-30 </p>