Parallel Algorithms of Well-Balanced and Weighted Average Flux for Shallow Water Model Using CUDA

Compute Unified Device Architecture (CUDA) implementations are presented of a well-balanced finite volume method for solving a shallow water model. The CUDA platform allows programs to run parallel on GPU. Four versions of the CUDA algorithm are presented in addition to a CPU implementation. Each version is improved from the previous one. We present the following techniques for optimizing a CUDA program: limiting register usage, changing the global memory access pattern, and using loop unroll. The accuracy of all programs is investigated in 3 test cases: a circular dam break on a dry bed, a circular dam break on a wet bed, and a dam break flow over three humps. The last parallel version shows 3.84x speedup over the first CUDA implementation. We use our program to simulate a real-world problem based on an assumed partial breakage of the Srinakarin Dam located in Kanchanaburi province, Thailand. The simulation shows that the strong interaction between massive water flows and bottom elevations under wet and dry conditions is well captured by the well-balanced scheme, while the optimized parallel program produces a 57.32x speedup over the serial version.

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A global shallow water model using high order multi-moment constrained finite volume method and icosahedral grid

Journal of Computational Physics ◽

10.1016/j.jcp.2009.11.008 ◽

2010 ◽

Vol 229 (5) ◽

pp. 1774-1796 ◽

Cited By ~ 40

Author(s):

Satoshi Ii ◽

Feng Xiao

Keyword(s):

Shallow Water ◽

Finite Volume Method ◽

Finite Volume ◽

High Order ◽

Water Model ◽

Shallow Water Model ◽

Volume Method

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1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method

Journal of Applied Mathematics ◽

10.1155/2012/489269 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 8

Author(s):

Szu-Hsien Peng

Keyword(s):

Shallow Water ◽

Finite Volume Method ◽

Finite Volume ◽

Shallow Water Equation ◽

Dam Break ◽

Flume Experiments ◽

One Dimensional ◽

Dam Break Flow ◽

The One ◽

Volume Method

The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative finite volume method, splitting is applied to manage the combination of hyperbolic term and source term of the shallow water equation and then to promote 1D to 2D. The simulations are validated by the comparison with flume experiments. Unsteady dam-break flow movement is found to be reasonably well captured by the model. The proposed concept could be further developed to the numerical calculation of non-Newtonian fluid or multilayers fluid flow.

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Coupled dam-break flow and bed load modelling using HLLC-WAF scheme

Water Science & Technology ◽

10.2166/wst.2015.324 ◽

2015 ◽

Vol 72 (7) ◽

pp. 1155-1167 ◽

Cited By ~ 1

Author(s):

Alireza Hosseinzadeh-Tabrizi ◽

Mahnaz Ghaeini-Hessaroeyeh

Keyword(s):

Experimental Data ◽

Weighted Average ◽

Dam Break ◽

Triangular Grid ◽

Governing Equations ◽

Mobile Bed ◽

Dam Break Flow ◽

Average Flux ◽

Comparison Of The Results ◽

Volume Method

A two-dimensional numerical model predicting flow over a mobile bed has been developed. Governing equations consist of the shallow water equations and the Exner equation. The finite volume method on an unstructured triangular grid was deployed to discretize the governing equations. The local Riemann problem is solved by the Harten, Lax and van Leer–contact (HLLC) method in the interface of the cells and the equations are solved using a fully coupled method. Then the flux modelling has been deployed by the total variation diminishing (TVD) version of the weighted average flux (WAF) scheme. The model was verified by comparison of the results and available experimental data for dam-break flow, in a laboratory test, via a channel with sudden enlargement and erodible bed conditions. Comparison of these two sets of results shows that increasing the accuracy of flux modelling caused the model results to have a reasonable agreement with the experimental data.

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Three-dimensional flow evolution after a dam break

Journal of Fluid Mechanics ◽

10.1017/s0022112010003599 ◽

2010 ◽

Vol 663 ◽

pp. 456-477 ◽

Cited By ~ 45

Author(s):

A. FERRARI ◽

L. FRACCAROLLO ◽

M. DUMBSER ◽

E. F. TORO ◽

A. ARMANINI

Keyword(s):

Experimental Data ◽

Free Surface ◽

Shallow Water ◽

Three Dimensional ◽

Dam Break ◽

Water Model ◽

Navier Stokes ◽

Finite Volume Scheme ◽

Shallow Water Model ◽

Weakly Compressible

In this paper, the wave propagation on a plane dry bottom after a dam break is analysed. Two mathematical models have been used and compared with each other for simulating such a dam-break scenario. First, the fully three-dimensional Navier–Stokes equations for a weakly compressible fluid have been solved using the new smooth particle hydrodynamics formulation, recently proposed by Ferrari et al. (Comput. Fluids, vol. 38, 2009, p. 1203). Second, the two-dimensional shallow water equations (SWEs) are solved using a third-order weighted essentially non-oscillatory finite-volume scheme. The numerical results are critically compared against the laboratory measurements provided by Fraccarollo & Toro (J. Hydraul. Res., vol. 33, 1995, p. 843). The experimental data provide the temporal evolution of the pressure field, the water depth and the vertical velocity profile at 40 gauges, located in the reservoir and in front of the gate. Our analysis reveals the shortcomings of SWEs in the initial stages of the dam-break phenomenon in reproducing many important flow features of the unsteady free-surface flow: the shallow water model predicts a complex wave structure and a wavy evolution of local free-surface elevations in the reservoir that can be clearly identified to be only model artefacts. However, the quasi-incompressible Navier–Stokes model reproduces well the high gradients in the flow field and predicts the cycles of simultaneous rapid decreasing and frozen stages of the free surface in the tank along with the velocity oscillations. Asymptotically, i.e. for ‘large times’, the shallow water model and the weakly compressible Navier–Stokes model agree well with the experimental data, since the classical SWE assumptions are satisfied only at large times.

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2D Shallow Water Model for Dam Break and Column Interactions

Journal of the Civil Engineering Forum ◽

10.22146/jcef.54307 ◽

2020 ◽

Vol 6 (3) ◽

pp. 237

Author(s):

Putu Indah Dianti Putri ◽

Rifqi Fauzan Iskandar ◽

Mohammad Bagus Adityawan ◽

Hadi Kardhana ◽

Dian Indrawati

Keyword(s):

Shallow Water ◽

Numerical Scheme ◽

Dam Break ◽

Water Model ◽

Navier Stokes ◽

Two Dimensional ◽

Navier Stokes Equation ◽

Saint Venant Equations ◽

Dam Break Flow ◽

Analytic Models

Dam break causes disastrous effects on the surrounding area, especially at the downstream, therefore, there is a need for accurate and timely predictions of dam break propagation to prevent both property damage and loss of life. This study aimed to determine the movement of dam-break flow in the downstream area by solving the Shallow Water Equations (SWE) or Saint Venant Equations which are based on the conservation of mass and momentum derived from Navier Stokes equation. The model was generated using a finite difference scheme which is the most common and simplest method for dam-break modeling while Forward Time Central Space (FTCS) numerical scheme was applied to simulate two-dimensional SWE. Moreover, the accuracy of the numerical model was checked by comparing its results with the analytic results of one-dimensional cases and a relatively small value of error was found in comparison to the analytic models as indicated with the RMSE values close to 0. The numerical to the two-dimensional models were also compared to a simple dam break in a flume and dam break with column interactions and the wave propagation in both cases was observed to become very close at a certain time. The model, however, used numerical filter (Hansen) to reduce the oscillations or numerical instability. The simulation and analysis, therefore, showed the ability of the numerical scheme of FTCS to resolve both cases of the simple dam break and dam break with column interactions in the Two-dimensional Shallow Water.

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Flood Simulation by a Well-Balanced Finite Volume Method in Tapi River Basin, Thailand, 2017

Modelling and Simulation in Engineering ◽

10.1155/2019/7053131 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13

Author(s):

Sutatip Vichiantong ◽

Thida Pongsanguansin ◽

Montri Maleewong

Keyword(s):

Shallow Water ◽

Finite Volume Method ◽

Finite Volume ◽

Water Model ◽

Interface Problem ◽

Reconstruction Technique ◽

Shallow Water Model ◽

Flood Simulation ◽

Southern Thailand ◽

Volume Method

Flood simulation of a region in southern Thailand during January 2017 is presented in this work. The study area covers the Tapi river, the longest river in southern Thailand. The simulation is performed by applying the two-dimensional shallow water model in the presence of strong source terms to the local bottom topography. The model is solved numerically by our finite volume method with well-balanced property and linear reconstruction technique. This technique is accurate and efficient at solving for complex flows in the wet/dry interface problem. Measurements of flows are collected from two gauging stations in the area. The initial conditions are prepared to match the simulated flow to the measurements recorded at the gauging stations. The accuracy of the numerical simulations is demonstrated by comparing the simulated flood area to satellite images from the same period. The results are in good agreement, indicating the suitability of the shallow water model and the presented numerical method for simulating floodplain inundation.

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