KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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Finite Element Analysis of River Flow Using SU/PG Scheme -I. Theory and Stability Analysis-

SU/PG 기법에 의한 하천흐름의 유한요소해석 -I. 이론 및 수치안정성 해석-

Han, Kun-Yeun;Baek, Chang-Hyun;Park, Kyung-Ok
한건연;백창현;박경옥

  • Published : 2004.05.31

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Abstract

The objective of this study is to develop a hydrodynamic model in a river by the SU/PG (Streamline Upwind/Petrov-Galerkin) scheme. A linear stability analysis is used to examine the amplification and phase characteristics of SU/PG based on this study for the linearized Saint Venant equations. Also, the finite element schemes such as BG (Bubnov-Galerkin), TG (Talyor-Galerkin), PG (Petrov-Galerkin) are used for the comparison of this scheme because of its underlying consistency and generality. Their results show the selective damping of short wave lengths and excellent phase accuracies achieved by the SU/PG method. Whereas the BG and TG schemes display less selective damping and poor phase accuracies, and BG scheme shows non-dissipative feature which causes a divergence problem in short wave length. Also, the SU/PG scheme displays slightly more damping and marginally improved phase accuracy in comparison with the PG method at a shorter wavelength. Therefore, the SU/PG scheme can be effectively applied to a wide variety of practical flow problems.

본 연구의 목적은 SU/PG(Streamline Upwind/Petrov-Galerkin) 기법에 의한 하천흐름 해석모형을 개발하기 위한 것으로 선형 안정성 해석을 통해 선형화된 Saint Venant 방정식에 대한 SU/PG 기법의 진폭 및 위상 특성을 검토하였다. SU/PG 기법과의 비교를 위해 BG(Bubnov-Galerkin), TG(Talyor-Galerkin), PG(Petrov-Galerkin)와 같은 유한요소 기법이 이용되었다. 해석결과, SU/PG 기법이 단파장에서의 선택적인 감쇠능력과 위상정확도에 있어 우수한 것으로 나타났다. 반면에 BG와 TG 기법은 선택적 감쇠능력과 위상정확도에서 열등한 것으로 나타났고, BG 기법은 단파장에서 발산 문제를 야기하는 것으로 나타났다. 또한, 더욱 짧은 파장에서는 SU/PG 기법이 PG 기법보다 좀더 감쇠적이고 부분적으로 향상된 위상정확도를 나타내었다. 따라서 SU/PG 기법이 다양한 실제적 흐름문제에 있어서 훨씬 이상적으로 적용될 수 있을 것으로 판단되었다.

Keywords

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