• Journal of Korea Water Resources Association
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• v.37 no.10
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• pp.845-855
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• 2004

The propagation and associated run-up process of nearshore tsunamis in the vicinity of shorelines have been analyzed by using a two-dimensional numerical model. The governing equations of the model are the nonlinear shallow-water equations. They are discretized explicitly by using a finite volume method and the numerical fluxes are reconstructed with a HLLC approximate Riemann solver and weighted averaged flux method. The model is applied to two problems; The first problem deals with water surface oscillations, while the second one simulates the propagation and subsequent run-up process of nearshore tsunamis. Predicted results have been compared to available analytical solutions and laboratory measurements. A very good agreement has been observed.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.1671-1676
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• 2006

홍수범람은 무제부에서의 하천수위 상승으로 인해 제내로 서서히 침수해가는 것과 월류로 인한 제방의 파괴를 동반하는 급격한 범람의 두 가지 형태가 있다. 기존연구들은 대부분이 월류에 의한 제방붕괴를 고려할 경우, 제방붕괴가 점진적으로 발생함에도 불구하고 이를 수치모형에 적용할 경우 갑작스럽게 지형을 낮추거나 초기지형으로써 제방붕괴를 가정하여 이를 고려해왔다. 본 연구에서는 제방붕괴를 시간의존적인 함수로 가정하고 이를 고려할 수 있는 서브프로그램의 개발을 통해 기존의 방법과 비교하여 그 영향을 검토하였다. 본 연구에 사용된 수치모형은 비선형의 2차원 천수방정식을 비구조적 격자계가 적용된 유한체적법을 이용하였으며, Riemann 해를 계산하기 위하여 approximate HLLC Riemann solver를 이용하였다. 기연구된 제방붕괴 고려방법과 본 연구의 시간의존적인 제방붕괴 고려방법을 통해 월류량을 비교하였을 때, 기존연구들의 홍수범람 해석결과가 과다예측 되었음을 알 수 있었다. 추후의 이루어질 연구들에서는 시간의존적인 제방붕괴를 반드시 고려해야됨과 동시에 이를 자연현상과 좀더 가깝고 효과적으로 고려할 수 있도록 연구가 필요하다.

• 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 Korea Water Resources Association
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• v.44 no.2
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• pp.109-123
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• 2011

In this study, 2D finite volume model, which can apply to the mixed meshes that is effective to treat the complicated topography such as a natural river, is developed. To do so, an algorithm for finding the neighbouring cell of a computational cell is introduced, and fluxes are computed using the HLLC approximate Riemann solver at each interface between a computational cell and it's neighbouring cells. Moreover, in order to numerically treat the bed slope which has important effect on the balance between flux gradients and sourte terms, different formula to compute the bed slope for rectangular and triangular mesh are applied. The developed model is applied to analyze dam-break in an experimental channel with $90^{\circ}$ bend and Malpasset dam-break in France. The two cases consist of mixed meshes and the suggested method is validated for the experimental channel and natural channel by comparison with the experimental data, field data and computed results.

• 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.32 no.1B
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• pp.21-27
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• 2012

The HLLL scheme, proposed by T. Linde, determines all the wave speeds from the initial states because the middle wave is evaluated by the introduction of a generalized entropy function. The scheme is considered a genuine successor to the original HLL scheme because it is completely separated form the Roe's linearization scheme unlike the HLLE scheme and does not rely on the exact solution unlike the HLLC scheme. In this study, a numerical model was configured by the HLLL scheme with the total energy as a generalized entropy function to solve governing equations, which are the one-dimensional shallow water equations without source terms and with an additional conserved variable relating a concentration. Despite the limitations of the first order solutions, results to three cases with the exact solutions were generally accurate. The HLLL scheme appeared to be superior in comparison with the other HLL-type schemes. In particular, the scheme gave fairly accurate results in capturing the front of wetting and drying. However, it revealed shortcomings of more time-consuming calculations compared to the other schemes.

• 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.

• Proceedings of the Korea Water Resources Association Conference
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• 2011.05a
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• pp.148-148
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• 2011

Riemann 문제는 천수방정식과 같은 쌍곡선형 방정식과 단일한 도약에 의해 불연속인 어떤 점의 좌 우에서 상수인 자료로 구성되는 초기치 문제로서 그 해법은 Godunov 방법과 같이 정확해에 의하면 정확 Riemann 해법, 근사 기법에 의하면 근사 Riemann 해법으로 불린다. 지금까지 이용되는 근사 Riemann 해법으로는 1981년에 P. L. Roe가 제안한 Roe의 선형화 기법과 1983년에 A. Harten, P. D. Lax, 그리고 B. van Leer가 제안한 HLL 기법의 수정 기법들이다. 최대 및 최소 파속만 고려하는 것으로 알려진 HLL 기법은 1988년에 B. Einfeldt의 제안에 의해 두 파속의 결정에서 Roe의 선형화 기법에 따른 고유치와 비교하는 것으로 수정되었다(HLLE 기법). 또한, 1994년에 E. F. Toro 등은 접촉파를 고려하기 위해 선형화된 지배방정식의 정확해로부터 중앙 파속을 고려하는 기법을 제안하였고, 이를 HLLC 기법으로 불렀다. 2002년에 T. Linde는 중앙 파속을 평가하기 위해 일반화된(수학적) 엔트로피 함수를 도입하였으며, van Leer는 이를 HLLL 기법으로 불렀다. 이 기법에서는 접촉파의 평가를 위해 보존변수에 대한 일반화된 엔트로피 함수로부터 중앙 파속이 유도되며, 이것과 특성 속도의 비교를 통해 최대 및 최소 파속이 결정된다. 따라서 이 기법에서는 모든 파속이 초기치로부터 결정되므로 HLLE 기법과 달리 Roe의 선형화 기법과 완전히 결별되고 HLLC 기법과 달리 정확해에 의존되지 않는 점에서 HLLL 기법은 모태인 HLL 기법의 온전한 계승으로 볼 수 있다. HLLL 기법은 여러 분야에 적용된 바 있으나, 수공학 분야에 적용된 사례는 알려진 바 없다. 이는 천수방정식에 대한 (물리적) 엔트로피 함수가 명확하지 않기 때문인 것으로 보인다. 이 연구에서는 보존변수로부터 정의되는 총 에너지를 일반화된 엔트로피 함수로 간주하여 모형을 구성하고, 정확해가 알려진 1차원 문제에 대해 적용성을 검토하였다. 정확해가 알려진 경우에 대해 모의한 결과, 1차 정도 수치해의 한계에도 불구하고, HLLL 기법의 결과는 대체로 정확해와 잘 일치하였으며 그 외의 HLL-형 기법의 그것에 비해 우수한 것으로 나타났다. 특히, 물이 빠져 바닥이 드러나는 상태에 대한 접촉 파속의 추정에서 Riemann 불변량을 이용하는 HLLC 기법에 비해 물이 빠지는 전선을 더 정확하게 포착하는 HLLL 기법의 결과는 매우 고무적이었다.

• 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.

• Journal of Korea Water Resources Association
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• v.47 no.11
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• pp.1061-1066
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• 2014

A stable second-order finite volume method was proposed to predict sediment transport under rapidly varied flow conditions such as transcritical flow. For the use under unsteady flow conditions, a sediment transport model was coupled with shallow water equations. HLLC approximate Riemann solver based on a monotone upstream-centered schemes for conservation laws (MUSCL) reconstruction was used for the computation of the flux terms. From the comparisons of dam break flow experiments on erodible beds in one- and two-dimensional channels, good agreements were obtained when proper parameters were provided. Lastly, dam surface erosion problem by overtopped water was simulated. Overall, the numerical solutions showed reasonable results, which demonstrated that the proposed numerical scheme could provide stable and physical results in the cases of subcritical and supercritical flow conditions.