• Title/Summary/Keyword: Shallow-water equations

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A Study on Simulation of Dam-break Wave Using Two-dimensional Finite Volume Model (2차원 유한체적모형을 이용한 댐 붕괴파 모의에 관한 연구)

  • Jeong, Woo-Chang;Park, Young-Jin
    • Journal of Korea Water Resources Association
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    • v.44 no.3
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    • pp.249-262
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    • 2011
  • In this study, in order to reduce the numerical oscillation due to the unbalance between source and flux terms as the HLLC scheme is applied to the flow analysis on the irregular bed topography, a unstructured finite volume model based on the well-balanced HLLC scheme and the shallow water equations is developed and applied to problems of dam-break waves. The well-balanced HLLC scheme considers directly the gradient of bed topography as the flux terms is calculated. This scheme provides the good numerical balance between the source and flux terms in the case of the application to the steady-state transcritical flow. To verify the numerical model developed in this study, it is applied to three cases of hydraulic model experiments and a field case study of Mapasset dam failure (France). As a result of the verification, the predicted numerical results agree relatively well with available laboratory and field measurements. The model provides slightly more accurate results compared with the existing models.

Analytical Comparison of Time-Dependent Mild-Slope Equations (시간의존 완경사방정식의 이론적 비교)

  • Lee, Chang-Hoon;James T. Kirby
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.6 no.4
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    • pp.389-396
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    • 1994
  • We analyze existing time-dependent mild-slope equations, which were developed by Smith and Sprinks (1975) (or, equivalently, Radder and Dingemans (1985)) and Kubo et al. (1992), in terms of the dispersion relation and energy transport. One-dimensionally in the horizontal direction, we compare the modulation of wave amplitudes for the time-dependent mild-slope equations against the linear Scrodinger equation. In view of the dispersion relation and modulation of wave amplitudes, Smith and Sprinks' model is more accurate in shallower water (kh$\leq$0.2$\pi$) and satisfies the linear Scrodinger equation in very shallow water (kh>0.2$\pi$) and satisfies the linear Scrodinger equation at a point of intermediate water depth (kh=0.3$\pi$). In view of the energy transport, Kubo et al.'s model is more accurate but yields singular solutions at some higher frequency range.

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Revaluation of Tsunami Risk at the Site of Ulchin Nuclear Power Plant (울진 원자력발전소 부지에 대한 지진해일 위험도 재평가)

  • 이해균;이대수
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.14 no.1
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    • pp.1-7
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    • 2002
  • In the past, safety assessment on the site of Ulchin Nuclear Power Plants against tsunamis was carried out with probable maximum earthquake magnitude and related tsunamigenic fault parameters. Recently, however, based on the seismic gap theory, some seismologists warned about earthquakes of larger magnitudes than had been expected. In this study, we revaluated tsunami risk with a finite difference model based on linear and nonlinear shallow water equations. Firstly, we simulated the\`83 tsunami and compared the calculated water surface profile with the observed wave heights. Secondly, we evaluated the rise and drop of sea water level at the site of Ulchin Nuclear Power Plant with fault parameters of the past '83, '93 tsunamis and some dangerous faults. Finally, we showed that the cooling water intake facility of Ulchin Nuclear Power Plants would be safely operated in disastrous tsunamis.

Development of Grid based Inundation Analysis Model (GIAM) (격자기반 침수해석모델(GIAM) 개발)

  • Lee, Byong Ju;Yoon, Seong Sim
    • Journal of Korea Water Resources Association
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    • v.50 no.3
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    • pp.181-190
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    • 2017
  • Population congestion and increasing porosity caused by urbanization and increasing rainfall intensity are the main reasons for urban inundation damage. In order to reduce the damage to urban flooding, it is necessary to take a inundation analysis model that can be considered the topographic impact (i.e., building and road) and simulate the detailed inundation areas. In this study, Grid based Inundation Analysis Model (GIAM) is developed using a two-dimensional shallow water equations. The study area is Gangnam basin, with a surface area of $7.4km^2$, which includes 5 drainage areas such as Nonhyun, Yeoksam, Seocho 1, 2, and 3. EPA SWMM5 is used for simulating the overflows at each manhole. GIAM model is constructed to allow for simulating a inundation area with 6 m grid size. The inundation analysis is conducted in two heavy rainfall events (Sep. 21, 2010 and July 27, 2011) for the model evaluation. The accuracy of the simulated inundation area is calculated 0.61 and 0.57 at POD index using the historical flooded area report. The developed model will be used as a tool for analyzing the flood prone areas based on rainfall scenario, and a tool for predicting the detailed inundation area in the real-time.

A Numerical Study on Characteristics of Flood Wave Passing through Urban Areas (2) : Application and Analysis (도시지역을 관통하는 홍수파의 특성에 관한 수치적 연구 (2) : 적용 및 분석)

  • Jeong, Woo-Chang;Cho, Yong-Sik;Lee, Jin-Woo
    • Journal of the Korean Society of Hazard Mitigation
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    • v.10 no.1
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    • pp.65-72
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    • 2010
  • In this study, the effects of urban areas against flood waves due to a dam failure were numerically investigated based on the two laboratory experiments and the predicted water surface elevations at specific points showed good agreement with available measurements. In the first experiment, a relatively high water depth and the delay effect of flow at the front of urban areas are observed. The urban areas may become a large obstacle against smooth propagation of flood wave. In the second one, as the inflow increases, moreover, the water surface elevations can be classified into abruptly decreasing portion and slowly decreasing portion, and the first arrival time to the front of urban area is decreasing with the increasing inflow.

Development of a Grid Based Two-Dimensional Numerical Method for Flood Inundation Modeling Using Globally-Available DEM Data (범용 DEM 데이터를 이용한 2차원 홍수범람 모형의 개발)

  • Lee, Seung-Soo;Lee, Gi-Ha;Jung, Kwan-Sue
    • Proceedings of the Korea Water Resources Association Conference
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    • 2010.05a
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    • pp.659-663
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    • 2010
  • In recent, flood inundation damages by hydraulic structure failures have increased drastically and thus a variety of countermeasures were needed to minimize such damages. A real-time flood inundation prediction technique is essential to protect and mitigate flood inundation damages. In the context of real time flood inundation modeling, this study aims to develop a grid based two-dimensional numerical method for flood inundation modeling using globally-available DEM data: SRTM with $90m{\times}90m$ spatial resolution. The newly-developed model guarantees computational efficiency in terms of geometric data processing by direct application of DEM for flood inundation modeling and also have good compatibility with various types of raster data when compared to a commercial model such as FLUMEN. The model, which employed the leap-frog algorithm to solve shallow water and continuity equations, can simulate inundating flow from channel to lowland and also returning flow from lowland to channel by comparing water levels between channel and lowland in real time. We applied the model to simulate the BaekSan levee break in the Nam river during a flood period from August 10 to 13, 2002. The simulation results had good agreements with the field-surveyed data in terms of inundated area and also showed physically-acceptable velocity vector maps with respect to inundating and returning flows.

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Spillway Design by Using Hydraulic and Numerical Model Experiment - Case Study of HwaBuk Multipurpose Dam (수리 및 수치모형실험을 이용한 여수로 설계 - 화북다목적댐)

  • Kim, Dae-Geun;Choi, Ji-Woong;Kim, Chang-Si;Lee, Ji-Won
    • Journal of Korea Water Resources Association
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    • v.38 no.3 s.152
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    • pp.179-188
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    • 2005
  • This study on the HwaBuk Multipurpose Dam showed that two- and three- dimensional numerical model experiments, as well as hydraulic model experiments, can be useful analysis tools for engineers. A commercially available RMA2, which solves the shallow water equations, and FLOW-3D, which solves the Reynolds averaged Navier-Stokes equations, were used to simulate the hydraulic model setup. Numerical simulation results on the following were compared with the hydraulic model results: the flow in the reservoir basin and the approaching channel; the discharge in the overflow weir; the water surface profiles in the rollway, chute, and stilling basin; and the pressure distributions in the rollway. It was shown that there is a reasonably good agreement between the numerical model and the hydraulic model for the most of computations. There were, however, some differences between the numerical simulation results and hydraulic model results for the hydraulic jump in the stilling basin because of air entrainment effect.

Rossby Waves and Beta Gyre Associated with Tropical Cyclone-scale Barotropic Vortex on the Sphere

  • Nam, Ye-Jin;Cheong, Hyeong-Bin
    • Journal of the Korean earth science society
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    • v.41 no.4
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    • pp.344-355
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    • 2020
  • Tropical cyclone scale vortices and associated Rossby waves were investigated numerically using high-resolution barotropic models on the global domain. The equations of the barotropic model were discretized using the spectral transform method with the spherical harmonics function as orthogonal basis. The initial condition of the vortex was specified as an axisymmetric flow in the gradient wind balance, and four types of basic zonal states were employed. Vortex tracks showed similar patterns as those on the beta-plane but exhibited more eastward displacement as they moved northward. The zonal-mean flow appeared to control not only the west-east translation but also the meridional translation of the vortex. Such a meridional influence was revealed to be associated with the beta gyre and the Rossby wave, which are formed around the vortex due to the beta effect. In the case of the basic zonal state of climatological mean, the meridional translation speed reached the maximum value when the vortex underwent recurving.

Estimation of Tsunami Run-up Heights with Parameters (매개변수에 따른 지진해일의 처오름높이 예측)

  • Ahn, Young-Chang;Hwang, Kyu-Nam;Cho, Yong-Sik
    • Journal of Korea Water Resources Association
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    • v.36 no.3 s.134
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    • pp.437-445
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    • 2003
  • Since many islands are located in the South Sea, unexpected damage by tsunamis could be caused by mutual interferences between adjacent islands. In this study, the variation of run-up heights is investigated by using different crest lengths of incident waves and different distances between two adjacent islands. The run-up height sharply increases when the crest length of Incident waves is greater than the distance bewteen outer boundaries of two islands. The run-up height also increases as the distance between two adjacent islands decreases.

2D Finite Element Modeling of Bed Elevation Change in a Curved Channel (유한요소법을 이용한 만곡수로에서의 2차원 하상변동 수치모형)

  • Kim Tae Beom;Choi Sung-Uk;Min Kyung Duck
    • Proceedings of the Korea Water Resources Association Conference
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    • 2005.05b
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    • pp.414-418
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    • 2005
  • A finite element model is developed for the numerical simulation of bed elevation change in a curved channel. The SU/PG (Streamline-Upwind/Petrov-Galerkin) method is used to solve 2D shallow water equations and the BG (Bubnov-Galerkin) method is used for the Exner equation. For the time derivative terms, the Crank-Nicolson scheme is used. The developed model is a decoupled model in a sense that the bed elevation does not change simultaneously with the flow during the computational time step. The total load formula with is used for the sediment transport model. The slip conditions are described along the lateral boundaries. The effects of gravity force due to geometry change and the secondary flows in a curved channel are considered in the model. For the verification, the model is applied to two laboratory experiments. The first is $140^{\circ}$ bended channel data at Delft Hydraulics Laboratory and the second is $140^{\circ}$ bended channel data at Laboratory of Fluid Mechanics of the Delft University of Technology. The finite element grid is constructed with linear quadrilateral elements. It is found that the computed results are in good agreement with measured data, showing a point bar at the inner bank and a pool at the outer bank.

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