• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.3B
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• pp.175-183
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• 2012

In this study, Galerkin scheme and SU/PG scheme of Petrov-Galerkin family were applied to the shallow water equations and a finite element model for shallow water flow was developed. Numerical simulations were conducted in several flumes with convection-dominated flow condition. Flow simulation of channel with slender structure in the water course revealed that Galerkin and SU/PG schemes showed similar results under very low Fr number and Re number condition. However, when the Fr number increased up to 1.58, Galerkin scheme did not converge while SU/PG scheme produced stable solutions after 5 iterations by Newton-Raphson method. For the transcritical flow simulation in diverging channel, the present model predicted the hydraulic jump accurately in terms of the jump location, the depth slope, and the flow depth after jump, and the numerical results showed good agreements with the hydraulic experiments carried out by Khalifa(1980). In the oblique hydraulic jump simulation, in which convection-dominated supercritical flow (Fr=2.74) evolves, Galerkin scheme blew up just after the first iteration of the initial time step. However, SU/PG scheme captured the boundary of oblique hydraulic jump accurately without numerical oscillation. The maximum errors quantified with exact solutions were less than 0.2% in water depth and velocity calculations, and thereby SU/PG scheme predicted the oblique hydraulic jump phenomena more accurately compared with the previous studies (Levin et al., 2006; Ricchiuto et al., 2007).

• 한국방재학회:학술대회논문집
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• 2011.02a
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• pp.198-198
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• 2011

The numerical simulation of dam break problem suffers from several challenges in terms of accuracy, stability, and versatility of the simulation algorithm since the water flow is generally discontinuous and presents abrupt variations. Thus, to obtain stable and accurate solutions, flow models for this purpose require numerical schemes provided with shock-capturing properties, and with the ability to work with flexible two-dimensional meshes. In this context, SU/PG method(Hughes and Brooks, 1979) is excellent candidate for the solution of the dam break problem. The weak formulation of the equations and the discontinuous polynomial basis lead to an accurate representation of bore waves(shocks). Furthermore, the discretization of the domain in finite elements is extremely effective in modeling complex geometries. In this study, a finite element model based on the SU/PG scheme is developed to solve shallow water equations and the model is applied to dam break problem. It is found that the present model accurately captures the bore wave that propagates downstream while spreading laterally and the depression wave that moves upstream. Furthermore, the propagation and formation of water surface profile compared favorably with those obtained by the previously published results.

• Proceedings of the Korea Water Resources Association Conference
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• 2003.05a
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• pp.485-488
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• 2003

• Journal of the Korean GEO-environmental Society
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• v.15 no.3
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• pp.41-48
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• 2014

Experimental study of sedimentation and self-weight consolidation has been primary research area in dredged soil. However, good quality of the dredged soil and minimum water pollution caused by the pumping of reclaimed soil require intensive study of the flow characteristics of dredged material due to dumping. In this study, continuity and the equilibrium equations for mass flow assuming single phase was derived to simulate mass flow in dredged containment area. To optimize computation and modeling time for three dimensional geometry and boundary conditions, depth integration is applied to governing equations to consider three dimensional topography of the site. Petrov-Galerkin formulation is applied in spatial discretization of governing equations. Generalized trapezoidal rule is used for time integration, and Newton iteration process approximated the solution. DG and CDG technique were used for weighting matrix in discontinuous test function in dredged flow analysis, and numerical stability was evaluated by performed a square slump simulation. A comparative analysis for numerical methods showed that DG method applied to SU / PG formulation gives minimal pseudo oscillation and reliable numerical results.

• Journal of Wetlands Research
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• v.13 no.3
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• pp.395-409
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• 2011

The objective of this study is to develop an accurate and robust two-dimensional finite element method for turbulence simulation in open channels. The model is based on Streamline Upwind/Petrov-Galerkin finite element method and Boussinesq's eddy viscosity theory. The method developed in the study is depth-averaged mixing length model which assumes anisotropic and local equilibrium state of turbulence. The model calibration and validation were performed by comparing with analytical solutions and observed data. Several numerical simulations were carried out, which examined the performance of the turbulence model for the purpose of sensitivity analysis. The uniform channels that appear horizontal flow and vertical flow were carried out. The model was also applied to the Han river was in for the applicability test. The results were compared with the observed data. The suggested model displayed reasonable flow distribution compare to the observed data in natural river flow. As a result of this study, the two-dimensional finite element model provides a reliable results for flow distribution based on the turbulence simulation in open channels.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.630-634
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• 2010

최근의 기후변화는 강우강도의 증가로 인한 홍수의 빈도 및 홍수량의 증가로 인한 홍수 피해의 증가를 유발하고 있으며, 갈수기 및 평수기의 유량감소로 인한 수질의 악화와 부유사의 증가로 인한 피해가 증가하고 있는 실정이다. 이러한 피해에 대한 대책으로는 기후변화를 유발하는 전 지구적인 온난화의 대책이 가장 선행되어야 하겠으며, 또한 이수, 치수를 위한 정확한 하천해석을 통한 하천관리가 매우 중요한 실정이다. 하천관리는 경제 산업적 측면에서 중요한 분야이며, 바람직한 하천관리를 위해서는 하천의 거동에 대한 정확한 해석이 필수적이다. 많은 흐름 해석에서 섬이나 하천 구조물의 주위에서 복잡한 2차원적인 하천 흐름의 특성을 잘 나타낸다. 2차원 수치모형들은 이러한 불규칙한 경계면에서 발생하는 난류흐름을 처리하는데 어려움이 있다. 이는 대부분의 실제하천이나 홍수파 해석, 댐 붕괴류 해석, 조수영향과 같은 해안공학의 문제에서도 발생한다. 본 연구에서 개발한 난류해석기법의 적용성을 검증하기 위하여 내부경계가 존재하는 실험하도에 대한 수치모의를 수행하고 결과를 실험치, 해석해와 비교를 통하여 모형의 적용성과 적정 난류교환계수를 선정하였다. 실측치와 비교검토를 통하여 본 연구에서 개발된 2차원 난류해석을 유한요소모형의 적용성을 검증하였다.

• Journal of Korea Water Resources Association
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• v.47 no.11
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• pp.1077-1086
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• 2014

The flood wave generated due to dam break is affected by initial depth upstream since it is related with hydraulic characteristics propagating downstream, and flow resistance stress has influence on the celerity, travel distance, and approaching depth of shock wave in implementing numerical simulation. In this study, a shallow water flow model employing SU/PG scheme was developed and verified by analytic solutions; propagation characteristics of dam break according to flow resistance and initial depth were analyzed. When bottom frictional stress was applied, the flow depth was relatively higher while the travel distance of shock wave was shorter. In the case of Coulomb stress, the flow velocity behind the location of dam break became lower compared with other cases, and showed values between no stress and turbulent stress at the reach of shock wave. The value of Froude number obtained by no frictional stress at the discontinuous boundary was the closest to 1.0 regardless of initial depth. The adaption of Coulomb stress gave more appropriate results compared with turbulent stress at low initial depth. However, as the initial depth became increased, the dominance of flow resistance terms was weakened and the opposite result was observed.