KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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Numerical Simulation of Depth-Averaged Flow with a CDG Finite Element Method

CDG 유한요소법을 이용한 수심적분 흐름의 수치모의

  • 김태범 (연세대학교 공과대학 사회환경시스템공학부) ;
  • 최성욱 (연세대학교 공과대학 사회환경시스템공학부) ;
  • 민경덕 (연세대학교 이과대학 지구시스템과학과)
  • Received : 2005.09.23
  • Accepted : 2006.07.26
  • Published : 2006.09.30
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Abstract

This paper presents a numerical model for the simulations of 2D depth-averaged flows. The shallow water equations are solved numerically by the Characteristic Dissipative Galerkin (CDG) finite element method. For validation, the developed model is applied to the hydraulic jump. The computed results are compared with the analytical solution, revealing good agreement. In addition, flow in a contracting channel showing standing waves is simulated. The calculated water surface profile appears to be qualitatively consistent with the observed data. The foregoing results indicate that the model is capable of simulating the abrupt change in flow field. Next, the model is applied to the flow in a $180^{\circ}$ curved channel. The simulated results show that the velocity near the inner bank is faster than that near the outer bank and the water depth near the inner bank is shallower than that near the outer bank. However, the simulated results show that the velocity distribution across the channel is almost uniform in the bend except the reach close to the end of the bend. This is due to the limitation of the governing equations in which the transverse convection of momentum by the secondary flows along a channel bend is not taken into account.

본 연구에서는 2차원 수심 적분된 흐름을 모의하기 위한 수치모델을 개발하였다. 유한요소법의 일종인 Characteristic Dissipative Galerkin(CDG) 기법을 적용시켜 천수방정식의 수치해를 구한다. 모델 검증을 위해서 1차원 도수문제에 적용하였고, 계산결과와 해석해를 비교할 때 만족스러운 결과를 얻었다. 정상파를 보이는 단면축소 수로에서의 흐름을 모의한 결과, 실험결과와 유사한 수면분포를 얻었다. 이러한 검증 과정을 통해서 본 수치모델을 이용하여 흐름영역이 갑작스럽게 변화하는 경우에도 모의 가능함을 알았다. 또한 $180^{\circ}$ 만곡수로에 적용한 결과, 만곡부 내측의 유속이 외측에 비해서 크며, 만곡부 내측의 수심은 외측에 비해서 작은 만곡부 흐름특성을 잘 나타내고 있다. 그러나 만곡수로에서 이차류에 의한 운동량의 횡방향 이송을 고려하지 않는 지배방정식의 한계점으로 인해서, 만곡부 끝단을 제외한 만곡부 전체에 걸쳐서 단면상의 종방향 유속이 일정한 분포를 보이고 있다.

Keywords

References

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