Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 9

shallow water equations Related Abstracts

9 Combined Effect of Moving and Open Boundary Conditions in the Simulation of Inland Inundation Due to Far Field Tsunami

Authors: Md. Fazlul Karim, M. Ashaque Meah, M. Shah Noor, Nazmun Nahar Papri, M. Khalid Hossen, M. Ismoen


Tsunami and inundation modelling due to far field tsunami propagation in a limited area is a very challenging numerical task because it involves many aspects such as the formation of various types of waves and the irregularities of coastal boundaries. To compute the effect of far field tsunami and extent of inland inundation due to far field tsunami along the coastal belts of west coast of Malaysia and Southern Thailand, a formulated boundary condition and a moving boundary condition are simultaneously used. In this study, a boundary fitted curvilinear grid system is used in order to incorporate the coastal and island boundaries accurately as the boundaries of the model domain are curvilinear in nature and the bending is high. The tsunami response of the event 26 December 2004 along the west open boundary of the model domain is computed to simulate the effect of far field tsunami. Based on the data of the tsunami source at the west open boundary of the model domain, a boundary condition is formulated and applied to simulate the tsunami response along the coastal and island boundaries. During the simulation process, a moving boundary condition is initiated instead of fixed vertical seaside wall. The extent of inland inundation and tsunami propagation pattern are computed. Some comparisons are carried out to test the validation of the simultaneous use of the two boundary conditions. All simulations show excellent agreement with the data of observation.

Keywords: Indonesian tsunami of 2004, open boundary condition, moving boundary condition, boundary-fitted curvilinear grids, far-field tsunami, shallow water equations, tsunami source

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8 Depth-Averaged Modelling of Erosion and Sediment Transport in Free-Surface Flows

Authors: Thomas Rowan, Mohammed Seaid


A fast finite volume solver for multi-layered shallow water flows with mass exchange and an erodible bed is developed. This enables the user to solve a number of complex sediment-based problems including (but not limited to), dam-break over an erodible bed, recirculation currents and bed evolution as well as levy and dyke failure. This research develops methodologies crucial to the under-standing of multi-sediment fluvial mechanics and waterway design. In this model mass exchange between the layers is allowed and, in contrast to previous models, sediment and fluid are able to transfer between layers. In the current study we use a two-step finite volume method to avoid the solution of the Riemann problem. Entrainment and deposition rates are calculated for the first time in a model of this nature. In the first step the governing equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed in conservative form and are used to calculate a solution that satisfies the conservation property. This method is found to be considerably faster than other comparative finite volume methods, it also exhibits good shock capturing. For most entrainment and deposition equations a bed level concentration factor is used. This leads to inaccuracies in both near bed level concentration and total scour. To account for diffusion, as no vertical velocities are calculated, a capacity limited diffusion coefficient is used. The additional advantage of this multilayer approach is that there is a variation (from single layer models) in bottom layer fluid velocity: this dramatically reduces erosion, which is often overestimated in simulations of this nature using single layer flows. The model is used to simulate a standard dam break. In the dam break simulation, as expected, the number of fluid layers utilised creates variation in the resultant bed profile, with more layers offering a higher deviation in fluid velocity . These results showed a marked variation in erosion profiles from standard models. The overall the model provides new insight into the problems presented at minimal computational cost.

Keywords: Sediment Transport, erosion, finite volume method, shallow water equations

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7 Comparison of Finite Difference Schemes for Numerical Study of Ripa Model

Authors: Sidrah Ahmed


The river and lakes flows are modeled mathematically by shallow water equations that are depth-averaged Reynolds Averaged Navier-Stokes equations under Boussinesq approximation. The temperature stratification dynamics influence the water quality and mixing characteristics. It is mainly due to the atmospheric conditions including air temperature, wind velocity, and radiative forcing. The experimental observations are commonly taken along vertical scales and are not sufficient to estimate small turbulence effects of temperature variations induced characteristics of shallow flows. Wind shear stress over the water surface influence flow patterns, heat fluxes and thermodynamics of water bodies as well. Hence it is crucial to couple temperature gradients with shallow water model to estimate the atmospheric effects on flow patterns. The Ripa system has been introduced to study ocean currents as a variant of shallow water equations with addition of temperature variations within the flow. Ripa model is a hyperbolic system of partial differential equations because all the eigenvalues of the system’s Jacobian matrix are real and distinct. The time steps of a numerical scheme are estimated with the eigenvalues of the system. The solution to Riemann problem of the Ripa model is composed of shocks, contact and rarefaction waves. Solving Ripa model with Riemann initial data with the central schemes is difficult due to the eigen structure of the system.This works presents the comparison of four different finite difference schemes for the numerical solution of Riemann problem for Ripa model. These schemes include Lax-Friedrichs, Lax-Wendroff, MacCormack scheme and a higher order finite difference scheme with WENO method. The numerical flux functions in both dimensions are approximated according to these methods. The temporal accuracy is achieved by employing TVD Runge Kutta method. The numerical tests are presented to examine the accuracy and robustness of the applied methods. It is revealed that Lax-Freidrichs scheme produces results with oscillations while Lax-Wendroff and higher order difference scheme produce quite better results.

Keywords: shallow water equations, finite difference schemes, Riemann problem, temperature gradients

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6 A Hybrid Artificial Intelligence and Two Dimensional Depth Averaged Numerical Model for Solving Shallow Water and Exner Equations Simultaneously

Authors: S. Mehrab Amiri, Nasser Talebbeydokhti


Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme.  In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.

Keywords: Artificial Neural Network, shallow water equations, morphodynamic model, sediment continuity equation

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5 A Finite Element/Finite Volume Method for Dam-Break Flows over Deformable Beds

Authors: Ashraf Osman, Mohammed Seaid, Alia Alghosoun


A coupled two-layer finite volume/finite element method was proposed for solving dam-break flow problem over deformable beds. The governing equations consist of the well-balanced two-layer shallow water equations for the water flow and a linear elastic model for the bed deformations. Deformations in the topography can be caused by a brutal localized force or simply by a class of sliding displacements on the bathymetry. This deformation in the bed is a source of perturbations, on the water surface generating water waves which propagate with different amplitudes and frequencies. Coupling conditions at the interface are also investigated in the current study and two mesh procedure is proposed for the transfer of information through the interface. In the present work a new procedure is implemented at the soil-water interface using the finite element and two-layer finite volume meshes with a conservative distribution of the forces at their intersections. The finite element method employs quadratic elements in an unstructured triangular mesh and the finite volume method uses the Rusanove to reconstruct the numerical fluxes. The numerical coupled method is highly efficient, accurate, well balanced, and it can handle complex geometries as well as rapidly varying flows. Numerical results are presented for several test examples of dam-break flows over deformable beds. Mesh convergence study is performed for both methods, the overall model provides new insight into the problems at minimal computational cost.

Keywords: Finite Element Method, finite volume method, hybrid techniques, shallow water equations, dam-break flows, deformable beds, linear elasticity

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4 Assessment of Golestan Dam Break Using Finite Volume Method

Authors: Ebrahim Alamatian, Seyed Mehdi Afzalnia


One of the most vital hydraulic structures is the dam. Regarding the unrecoverable damages which may occur after a dam break phenomenon, analyzing dams’ break is absolutely essential. GOLESTAN dam is located in the western South of Mashhad city in Iran. GOLESTAN dam break might lead to severe problems due to adjacent tourist and entertainment areas. In this paper, a numerical code based on the finite volume method was applied for assessing the risk of GOLESTAN dam break. As to this issue, first, a canal with a triangular barrier was modeled so as to verify the capability of the concerned code. Comparing analytical, experimental and numerical results showed that water level in the model results is in a good agreement with the similar water level in the analytical solutions and experimental data. The results of dam break modeling are revealed that two of the bridges, that are PARTOIE and NAMAYESHGAH, located downstream in the flow direction, are at risk following the potential GOLESTAN dam break. Therefore, the required times to conduct the precautionary measures at bridges were calculated at about 12 and 21 minutes, respectively. Thus, it is crucial to announce people about the possible risks of the dam break in order to decrease likely losses.

Keywords: numerical model, shallow water equations, GOLESTAN dam break, dry and wet beds modeling

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3 Flood Modeling in Urban Area Using a Well-Balanced Discontinuous Galerkin Scheme on Unstructured Triangular Grids

Authors: Rabih Ghostine, Craig Kapfer, Viswanathan Kannan, Ibrahim Hoteit


Urban flooding resulting from a sudden release of water due to dam-break or excessive rainfall is a serious threatening environment hazard, which causes loss of human life and large economic losses. Anticipating floods before they occur could minimize human and economic losses through the implementation of appropriate protection, provision, and rescue plans. This work reports on the numerical modelling of flash flood propagation in urban areas after an excessive rainfall event or dam-break. A two-dimensional (2D) depth-averaged shallow water model is used with a refined unstructured grid of triangles for representing the urban area topography. The 2D shallow water equations are solved using a second-order well-balanced discontinuous Galerkin scheme. Theoretical test case and three flood events are described to demonstrate the potential benefits of the scheme: (i) wetting and drying in a parabolic basin (ii) flash flood over a physical model of the urbanized Toce River valley in Italy; (iii) wave propagation on the Reyran river valley in consequence of the Malpasset dam-break in 1959 (France); and (iv) dam-break flood in October 1982 at the town of Sumacarcel (Spain). The capability of the scheme is also verified against alternative models. Computational results compare well with recorded data and show that the scheme is at least as efficient as comparable second-order finite volume schemes, with notable efficiency speedup due to parallelization.

Keywords: Flood Modeling, shallow water equations, dam-break, discontinuous Galerkin scheme

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2 Impact of Data and Model Choices to Urban Flood Risk Assessments

Authors: Abhishek Saha, Serene Tay, Gerard Pijcke


The availability of high-resolution topography and rainfall information in urban areas has made it necessary to revise modeling approaches used for simulating flood risk assessments. Lidar derived elevation models that have 1m or lower resolutions are becoming widely accessible. The classical approaches of 1D-2D flow models where channel flow is simulated and coupled with a coarse resolution 2D overland flow models may not fully utilize the information provided by high-resolution data. In this context, a study was undertaken to compare three different modeling approaches to simulate flooding in an urban area. The first model used is the base model used is Sobek, which uses 1D model formulation together with hydrologic boundary conditions and couples with an overland flow model in 2D. The second model uses a full 2D model for the entire area with shallow water equations at the resolution of the digital elevation model (DEM). These models are compared against another shallow water equation solver in 2D, which uses a subgrid method for grid refinement. These models are simulated for different horizontal resolutions of DEM varying between 1m to 5m. The results show a significant difference in inundation extents and water levels for different DEMs. They are also sensitive to the different numerical models with the same physical parameters, such as friction. The study shows the importance of having reliable field observations of inundation extents and levels before a choice of model and data can be made for spatial flood risk assessments.

Keywords: Flooding, DEM, shallow water equations, subgrid

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1 An Optimal Control Method for Reconstruction of Topography in Dam-Break Flows

Authors: Mohammed Seaid, Alia Alghosoun, Nabil El Moçayd


Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Keywords: Finite Element Method, finite volume method, shallow water equations, nonlinear elasticity, erodible beds, stresses in soil

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