• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.2
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• pp.479-492
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• 2014

In this study, was proposed a numerical scheme imposing exact solutions as the internal boundary conditions for the shallow-water flows over a discontinuous transverse structure such as a step. The HLLL approximate Riemann solver with the MUSCL was used for the test of the proposed scheme. Very good agreement was obtained between simulations and exact solutions for various problems of the shallow-water flows over a step. In addition, results by the numerical model showed good agreement with those of dam-break experiments over a step and stepped chute one. Developed model can simulate the shallow-water flows over discontinuous bottom such as a drop structure without additional rating curve or topography smoothing. Given the proper evaluations for the flow resistance by a step and the energy loss by the nappe flow in the future, could be simulated flooding and drying of the shallow-water flows over discontinuous topography such as a weir or the river road with retaining wall.

• 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.

• 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.

• Journal of Korea Water Resources Association
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• v.48 no.11
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• pp.957-967
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• 2015

It was reviewed for the 2D numerical simulations to evaluate the effects of flood control by detention basin, even if stage-discharge relationships for the side weir were not known. A 2D depth-integrated numerical model was constructed by the application of the finite volume method to the shallow water equations as a numerical method and the introduction of an approximate Riemann solver for the accurate calculation of fluxes. Results by the model were compared with those by the laboratory test for the cases of free overflow and submerged flow over a side weir between the channel and storage. The difference between simulated and measured discharge coefficients for the case of free overflow is very small. In addition, the results by simulations were in good agreement with those by experiments for the submerged flow over a side weir and its mechanism was reproduced well. Through this study the discharge coefficients of side weirs can be accurately determined by the 2D numerical model and a considerable degree of accuracy can be achieved to evaluate the effect of flood defenses by detention basins. Thus, it will be expected to apply this model practically to the plan of detention basins, the evaluation of design alternatives, or the management of the existing ones.

• 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 for Aeronautical & Space Sciences
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• v.35 no.3
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• pp.183-195
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• 2007

Comprehensive mathematical comparison of numerical dissipation vector was made for a compressible and the preconditioned version Roe's Riemann solvers. Choi and Merkle type preconditioning method was selected from the investigation of the convergence characteristics of the various preconditioning methods for the flows over a two-dimensional bump. The investigation suggests a way of migration from a compressible code to a preconditioning code with a minor changes in Eigenvalues while maintaining the same code structure. Von Neumann stability condition and viscous Jacobian were considered additionally to improve the stability and accuracy for the viscous flow analysis. The developed code was validated through the applications to the standard validation problems.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5B
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• pp.429-439
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• 2009

When Catastrophic extreme flood occurs due to dam break, the response time for flood warning is much shorter than for natural floods. Numerical models can be powerful tools to predict behaviors in flood wave propagation and to provide the information about the flooded area, wave front arrival time and water depth and so on. But flood wave propagation due to dam break can be a process of difficult mathematical characterization since the flood wave includes discontinuous flow and dry bed propagation. Nevertheless, a lot of numerical models using finite volume method have been recently developed to simulate flood inundation due to dam break. As Finite volume methods are based on the integral form of the conservation equations, finite volume model can easily capture discontinuous flows and shock wave. In this study the numerical model using Riemann approximate solvers and finite volume method applied to the conservative form for two-dimensional shallow water equation was developed. The MUSCL scheme with surface gradient method for reconstruction of conservation variables in continuity and momentum equations is used in the predictor-corrector procedure and the scheme is second order accurate both in space and time. The developed finite volume model is applied to 2D partial dam break flows and dam break flows with triangular bump and validated by comparing numerical solution with laboratory measurements data and other researcher's data.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1961-1971
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• 2006

A soft recovery system (SRS) is a device that stops a high speed projectile without damaging the projectile. The SRS is necessary to verify the shock resistant requirements of microelectronics and electro-optic sensors in smart munitions, where the projectiles experience over 20,000 g acceleration inside the barrel. In this study, a computer code for the performance evaluation of a SRS based on ballistic compression decelerator concept has been developed. It consists of a time accurate compressible one-dimensional Euler code with use of deforming grid and a projectile motion analysis code. The Euler code employs Roe's approximate Riemann solver with a total variation diminishing (TVD) method. A fully implicit dual time stepping method is used to advance the solution in time. In addition, the geometric conservation law (GCL) is applied to predict the solutions accurately on the deforming mesh. The equation of motion for the projectile is solved with the four-stage Runge-Kutta time integration method. A small scale SRS to catch a 20 mm bullet fired at 500 m/s within 1,600 g-limit has been designed with the proposed method.