• Journal of Korea Water Resources Association
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• v.36 no.5
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• pp.777-785
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• 2003

A numerical model for the solution of two-dimensional free surface flow is developed on unstructured grid. By using fractional step method, the two-dimensional shallow water equations (SWE) are treated as two one-dimensional problems. Thus, it is possible to simulate computational hydraulic problems with higher computational efficiency. The one-dimensional problems are solved using upwind TVD version of second-order Weighted Averaged Flux (WAF) scheme with HLLC approximate Riemann solver. The numerical oscillations which are common with second-order numerical scheme are controlled by exploiting WAF flux limiter, Some idealized test problems are solved using this model and very accurate and stable solutions are obtained. It can be concluded as an efficient implement for the computation of SWE including dam break problems that concerning discontinuities, subcritical and supercritical flows and complex domain.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2B
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• pp.121-129
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• 2009

In this study, dam-break flows are simulated numerically by using an efficient and accurate Cartesian cut-cell mesh system. In the system, most of the computational domain is discretized by the Cartesian mesh, while peculiar grids are done by a cutcell mesh system. The governing equations are then solved by the finite volume method. An HLLC approximate Riemann solver and TVD-WAF method are employed to calculation of advection flux of the shallow-water equations. To validate the numerical model, the model is applied to some problems such as a steady flow convergence on an ideal bed, a steady flow over an irregular bathymetry, and a rectangular tank problem. The present model is finally applied to a simulation of dam-break flow on an experimental channel. The predicted water surface elevations are compared with available laboratory measurements. A very reasonable agreement is observed.

• Journal of Korea Water Resources Association
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• v.36 no.4
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• pp.597-608
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• 2003

A transcritical flow occurs when the width and slope of a channel are varying abruptly. In this study, the transcritical flow in a two-dimensional open channel is analyzed by using the shallow-water equations. A weighted average flux scheme that has flux limiter with a total variation diminishing condition is introduced for a second-order accuracy in time and space, and non- spurious oscillations at discontinuous points. A HLLC method with three wane speeds is employed to calculate the Riemann problem. To overcome difficulties resulting from variation of channel sections in a two-dimensional analysis of transcritical flow, the numerical model is developed based on a generalized grid system.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.3
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• pp.69-78
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• 2007

In this study, a time-dependent aspect of an embankment failure is considered to simulate a flood inundation map and calculate overtopping discharge induced by an embankment failure. A numerical model has been developed by solving the two dimensional nonlinear shallow water equations with a finite volume method on unstructured grids. To analyze a Riemann problem, the HLLC approximate Riemann solver and the Weighted Averaged Flux method are employed by using a TVD limiter and the source term treatment is also employed by using the operator splitting method. Firstly, the numerical model is applied to a dam break problem and a sloping seawall. Obtained numerical results show good agreements with experimental data. Secondly, the model is applied to a flow induced by an embankment failure by assuming that the width and elevation of embankment are varied with time-dependent functions. As a result of the comparison with each numerical overtopping discharge, established flood inundation discharges in the previous studies are overestimated than the result of the present numerical model.

• Journal of the Korean Society of Hazard Mitigation
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• v.8 no.4
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• pp.91-100
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• 2008

Numerical implementation with a Cartesian cut-cell method is conducted in this study. A Cartesian cut-cell method is an easy and efficient mesh generation methodology for complex geometries. In this method, a background Cartesian grid is employed for most of computational domain and a cut-cell grid is applied for the peculiar grids where the flow characteristics are changed such as solid boundary to enhance the accuracy, applicability and efficiency. Accurate representation of complex geometries can be obtained by using the cut-cell method. The cut-cell grids are constructed with irregular meshes which have various shape and size. Therefore, the finite volume method is applied to numerical discretization on a irregular domain. The HLLC approximate Riemann solver, a Godunov-type finite volume method, is employed to discretize the advection terms in the governing equations. The weighted average flux method applied on the Cartesian cut cell grid for stabilization of the numerical results. To validate the numerical model using the Cartesian cut-cell grids, the model is applied to the rectangular tank problem of which the exact solutions exist. As a comparison of numerical results with the analytical solutions, the numerical scheme well represents flow characteristics such as free surface elevation and velocities in x-and y-directions in a rectangular tank with the Cartesian and cut-cell grids.

• Water Engineering Research
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• v.3 no.1
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• pp.23-30
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• 2002

A numerical model for the solution of two-dimensional dam break problems using fractional step method is developed on unstructured grid. The model is based on second-order Weighted Averaged Flux(WAF) scheme with HLLC approximate Riemann solver. To control the nonphysical oscillations associated with second-order accuracy, TVD scheme with SUPERBEE limiter is used. The developed model is verified by comparing the computational solutions with analytic solutions in idealized test cases. Very good agreements have been achieved in the verifications.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1752-1756
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• 2008

A simple, accurate and efficient mesh generation technique, the cut-cell method, is able to represent an arbitrarily complex geometry. Both structured and unstructured grid meshes are used in this method. First, the numerical domain is constructed with regular Cartesian grids as a background grid and then the solid boundaries or bodies are cut out of the background Cartesian grids. As a result, some boundary cells can be contained two numerical conditions such as the flow and solid conditions, where the special treatment is needed to simulate such physical characteristics. The HLLC approximate Riemann solver, a Godunov-type finite volume method, is employed to discretize the advection terms in the governing equations. Also, the TVD-WAF method is applied on the Cartesian cut-cell grids to stabilize numerical results. Present method is validated for the rectangular dam break problems. Initially, a conventional grid is constructed with the Cartesian regular mesh only and then applied to the dam-break flow simulation. As a comparative simulation, a cut-cell grids are applied to represent the flow domain rotated with arbitrary angles. Numerical results from this study are compared with the results from the case of the Cartesian regular mesh only. A good agreement is achieved with other numerical results presented in the literature.

• Water Engineering Research
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• v.3 no.1
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• pp.57-62
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• 2002

This research is intended to integrate long-term operation rules and real time operation policy for conservation & flood control in a reservoir. The familiar Yield model has been modified and used to provide long-term rule curves. The model employs linear programming technique under given physical conditions, i.e., total capacity, dead storage, spillways, outlet capacity and their respective elevations to find required and desired minimum storage fur different demands. To investigate the system behavior resulting from the above-mentioned operating policy, i.e., the rule curves, the simulation model was used. Results of the simulation model show that the results of the optimization model are indeed valid. After confirmation of the above mentioned rule curves by the simulation models, gate operation procedure was merged with the long term operation rules to determine the optimum reservoir operating policy. In the gate operation procedure, operating policy in downstream flood plain, i.e., determination of damaging and non-damaging discharges in flood plain, peak floods, which could be routed by reservoir, are determined. Also outflow hydrograph and variations of water surface levels for two known hydrographs are determined. To examine efficiency of the above-mentioned models and their ability in determining the optimum operation policy, Esteghlal reservoir in Iran was analyzed as a case study. A numerical model fur the solution of two-dimensional dam break problems using fractional step method is developed on unstructured grid. The model is based on second-order Weighted Averaged Flux(WAF) scheme with HLLC approximate Riemann solver. To control the nonphysical oscillations associated with second-order accuracy, TVD scheme with SUPERBEE limiter is used. The developed model is verified by comparing the computational solutions with analytic solutions in idealized test cases. Very good agreements have been achieved in the verifications.