• Journal of Korea Water Resources Association
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• v.43 no.1
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• pp.105-117
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• 2010

This paper presents a new and simple technique to perform MUSCL reconstruction for solving 2D shallow water equations. The modified MUSCL scheme uses weighted area ratio to apply non-uniform grid in stead of the previous method that equally distributed the difference of conservation variables to each interface. The suggested method can physically reconstruct conservation variables in case of uniform grid as well as non-uniform grid. In this study, Unsplit scheme applicable to unstructured grid is used and efficient slope limiter of TVD scheme is used to control numerical oscillation which can be occurred in modified MUSCL scheme. For accurate and efficient treatment of bed slope term, the modified MUSCL scheme is coupled with the surface gradient method. The finite volume model applied to suggested scheme is verified through a comparison between numerical solution and laboratory measurements data such as the simulations of isolated building test case and Bellos's dam break test case.

• Journal of Korea Water Resources Association
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• v.31 no.3
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• pp.279-290
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• 1998

The height and speed of the shock wave are critical data in flood-control operations or in the design of channel walls and bridges along rivers with high flow velocities. Therefore, a numerical model is needed for simulating flow discontinuity over a wide range of conditions. In this study, a governing equation. As a Riemann solver Roe(1981)'s one is used. The model employs the modified MUSCL for handling the unstructured grids in this research. this model that adopts the explicit tradditional twl dimmensional dam break problems, two hydraulic dam break model is simulations, and a steady state simulation in a curved channel. Conclusions of this research are as follows : 1) the finite volume method can be combined with the Godonov-type method that is useful for modeling shocks. Hence, the finite volume method is suitable for modeling shocks. 2) The finite volume model combined with the modified MUSCL is successful in modeling shock. Therefore, modified MUSCL is proved to be valid.

• Journal of Korea Water Resources Association
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• v.44 no.10
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• pp.819-830
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• 2011

The multi-slope MUSCL, proposed by T. Buffard and S. Clain, determines slopes of conserved variables at each edge of a cell in the linear reconstructions of data. In this study, the second order accurate numerical model was developed according to the multi-slope MUSCL to solve the shallow water equations on the unstructured grids. The HLLL scheme of approximate Riemann solvers was used to calculate fluxes. For the review of the applicability of the developed model, the results of the model were compared to the 'isolated building test' and the 'model city flooding experiment' conducted as part of the IMPACT (Investigation of extreMe flood Processes And unCerTainty) project in Europe. There were limitations to predict abrupt rising of water depths by the resistance of model buildings and water depths at the specific locations among the buildings. But they were identified as the same problems also revealed in results of the other models to the same experiment. On the more refined meshes to the 'model city flooding experiment' simulated results showed good agreement with measurements. It was verified that the developed model simulated well the complex phenomena such as a dam-break problem and the urban inundation by flash floods.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.8
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• pp.693-698
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• 2007

A numerical method for accurate simulations of rotor aerodynamics is proposed. The numerical diffusion in the typically coarse grids away from the rotor blades is improved by implying a fourth-order of interpolation of local characteristic variables of the flow in the reconstruction stage of MUSCL approach in the framework of a finite volume formulation. In addition, different slope limiters are applied to the different characteristic fields, such as compressive limiters to linear characteristic fields to reduce the numerical dissipation whereas, diffusive limiters to nonlinear characteristic fields to increase numerical stability. Various exemplary problems related to the rotor aerodynamics applications are tested and the numerical results show a significant improvement in wake capturing capability. However, rotor aeroacoustic calculations show no meaningful difference over traditional MUSCL approach.

• Proceedings of the Korea Water Resources Association Conference
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• 2011.05a
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• pp.158-158
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• 2011

천수방정식과 같은 쌍곡선형 미분방정식의 불연속 해에 대한 Riemann 해법은, 1950년대 말 공기동역학 분야에서 S. K. Godunov의 선구적인 시도 이후, 다양한 영역에서 성공적으로 적용되고 있다. 당초 제안된 해법은 공간에 대해 1차 정도였으나, 2차의 정도를 얻을 수 있는 기법이 1970년대 말 B. van Leer에 의해 제안되었으며, MUSCL로 불린다. 서로 인접한 격자의 보존변수가 고려된 경사가 도입되어 두 격자에 의해 공유되는 변의 좌 우에서 선형으로 보존변수가 재구축되는 MUSCL은 제한자와 함께 이용될 때, 구조 격자 체계에서 비교적 단순하면서도 효과적인 적용성이 입증되었다. 그런데, 이 기법을 2차원의 비구조 격자 체계에 적용하는 경우, 인접한 모든 격자의 보존변수를 고려한 평면의 경사를 결정해야 하는 어려움이 따른다. 특히, 삼각형 비구조 격자에 적용할 경우 최적의 평면을 결정하기 위해 Green-Gauss 적분식이나 최소-자승법 등을 이용하게 된다. 이에 비해, 2010년 T. Buffard와 S. Clain이 제안한 다중경사 기법은 격자의 각 변에서 경사가 각각 결정되는 방법으로 계산량이 많은 Green-Gauss 적분식이나 최소자승법을 피할 수 있는 장점이 있는 것으로 알려져 있다. 정확해가 알려진 두 경우에 대해 몇 가지 제한자를 적용한 결과를 1차 정도의 해와 함께 비교하였으며, superbee 제한자에 의한 결과가 우수하였으나, 희유파와 충격파가 맞닿는 곳에서 수치 분산이 나타났다. minmod 제한자의 결과가 대체로 무난하였으며, 이를 2차원 댐 붕괴 문제에 적용하여 1차 정도의 해와 비교하였다. 마찰이 없고 초기 수심이 댐 상류에서 10 m, 하류에서 5 m로서 물이 차 있는 경우, 1차 정도의 해에서 나타나는 수치 소산이 2차 정도에서는 발생되지 않았다. 댐 하류에서 초기에 수심이 영으로 바닥이 드러난 경우에서 마찰의 영향을 검토하였다. 마찰이 있는 경우, 마찰 경사 항의 Manning 계수를 0.04로 두었으며, 마찰에 의한 영향이 잘 드러났다. 수심이 50 mm 보다 작은 경우에는 마찰을 적용하지 않았다. 이 연구는 환경부 '차세대 핵심환경기술개발 사업'의 지원에 의한 것이다.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.30 no.4
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• pp.143-152
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• 2018

Numerical convergence and stability of TVD schemes have been applied in the FUNWAVE-TVD model were compared. The fourth order accurate MUSCL-TVD scheme using minmod limiter suggested by Yamamoto and Daiguji (1993), the fourth order accurate MUSCL-TVD scheme using van-Leer limiter suggested by Erduran et al. (2005) and the second order accurate MUSCL-TVD scheme using van-Leer limiter in Zhou et al. (2001) were compared. Comparisons of the numerical scheme were conducted with experimental data of Vincent and Briggs irregular wave experiments. In comparison with the fourth order accurate scheme using van-Leer limiter, the fourth order accurate scheme using minmod limiter is less dissipative but required lower CFL condition for stable numerical solution. On the other hand, the scheme using van-Leer limiter required smaller resolution spatial grid due to numerical dissipation, but relatively higher CFL condition can be used compared to the scheme using minmod limiter. In the breaking wave experiments which were conducted using high resolution spatial grid to reduce numerical dissipation, the characteristic of the schemes can be clearly observed. Numerical instabilities and blow-up of the numerical solutions were found in the irregular wave breaking simulation with the scheme using minmod limiter. However, the simulation can be completed with the scheme using van-Leer limiter, but required low CFL condition. Good agreements with the observed data were also observed in the results using van-Leer limiter.

• Journal of Korea Water Resources Association
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• v.36 no.1
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• pp.1-11
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• 2003

This paper describes a finite volume, two-dimensional model. It adopts a recently developed essentially non-oscillatory(ENO) schemes based on the Lax-Friedrichs solver, which was modified for a finite volume grid, and employs a modified MUSCL(Monotonic Upstream centered Scheme for Conservation Law) for second-order accuracy in space. To demonstrate the applications of the model, it is applied to solve the 1-D and 2-D dam-break problems. The model in conjunction with the modified MUSCL showed a better agreement with analytical solutions than the minmod function in 1-D dam-break problems and is satisfactorily validated with documented published data in 2-D dam-break problems. The model was applied to tidal wane entering channel at one end, and the results showed a good agreement with analytical solutions. In the channel with reflective boundary conditions specified at the extremities, the model was capable of accurately simulating the wave propagation.

• Journal of computational fluids engineering
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• v.15 no.2
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• pp.55-61
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• 2010

A dependence of weighting parameter in preconditioning method for solving low Mach number flow with incompressible flow nature is investigated. The present preconditioning method employs a finite-difference method applied Roe‘s flux difference splitting approximation with the MUSCL-TVD scheme and 4th-order Runge-Kutta method in curvilinear coordinates. From the computational results of benchmark flows through a 2-D backward-facing step duct it is confirmed that there exists a suitable value of the weighting parameter for accurate and stable computation. A useful method to determine the weighting parameter is introduced. With this method, high accuracy and stable computational results were obtained for the flow with low Mach number in the range of Mach number less than 0.3.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.291-306
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• 2011

We consider the second order Strang splitting method to approximate the solution to the KdV equation. The model equation is split into three sets of initial value problems containing convection and dispersal terms separately. TVD MUSCL or MUSCL scheme is applied to approximate the convection term and the second order centered difference method to approximate the dispersal term. In time stepping, explicit third order Runge-Kutta method is used to the equation containing convection term and implicit Crank-Nicolson method to the equation containing dispersal term to reduce the CFL restriction. Several numerical examples of weakly and strongly dispersive problems, which produce solitons or dispersive shock waves, or may show instabilities of the solution, are presented.

• Journal of computational fluids engineering
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• v.10 no.1
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• pp.99-106
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• 2005

Performance of first, second and third order accurate methods for calculation of in viscid fluxes in fluid flow governing equations are investigated here. For the purpose, an upwind method based on Roe's scheme is used to solve 2-dimensional Euler equations. To increase the accuracy of the method two different schemes are applied. The first one is a second and third order upwind-based algorithm with the MUSCL extrapolation Van Leer (1979), based on primitive variables. The other one is an upwind-based algorithm with the Chakravarthy extrapolation to the fluxes of mass, momentum and energy. The results show that the thickness of shock layer in the third order accuracy is less than its value in second order. Moreover, applying limiter eliminates the oscillations near the shock while increases the thickness of shock layer especially in MUSCL method using Van Albada limiter.