한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제46권2호
  • /
  • Pages.139-153
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  • 2013
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  • 2799-8746(pISSN)
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  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
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고르지 않은 바닥을 지나는 천수 흐름에 대한 유한체적 모형

Finite-Volume Model for Shallow-Water Flow over Uneven Bottom

  • 황승용 (한국건설기술연구원 수자원.환경연구본부 하천해안연구실)
  • 투고 : 2012.09.04
  • 심사 : 2012.10.11
  • 발행 : 2013.02.28
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초록

고르지 않은 바닥을 지나는 천수 흐름을 해석하기 위해 천수방정식의 흐름률 경사항과 바닥 경사 생성항에 대해 HLLL 기법과 DFB(Divergence Form for Bed slope source term) 기법을 각각 적용하여 유한체적 모형을 구성하였다. 또한, PSC(Partially Submerged Cell)의 고려를 위해 VFR(Volume/Free-surface Relationship)도 이용하였다. MUSCL에서 WSDGM(Weighted Surface-Depth Gradient Method)을 보다 단순하게 고쳐도 원래의 방법과 정확도가 동등함을 1차원 정상 흐름에 대해 확인하였다. 1차원 PSC에 대한 VFR를 통해 흐름률 경사항과 바닥 경사 생성항의 선평형성이 정확하게 충족됨을 입증하였다. 2차원 PSC에서 DFB 기법으로는 지배방정식의 선평형성이 충족되지 않은 문제를 삼각형 격자에 대한 VFR를 이용하여 해소하였다. 삼각형 턱과 둥근 융기를 지나는 2차원 댐 붕괴 흐름에 대한 모의에서 실험실 실험 결과와 잘 부합됨을 확인하였다. 또한, 부분 댐 붕괴 흐름에 대한 모형의 적용에서 경사면은 물론 불규칙 바닥에서도 요철의 잠김이 성공적으로 모의되었다. 따라서 고르지 않은 실제 하천 지형에 대한 이 모형의 적용성이 기대된다.

For analyzing shallow-water flows over the uneven bottom, the HLLL scheme and the divergence form for bed slope source term (DFB) technique, respectively were applied to the flux gradient and the bottom gradient source terms in a finite-volume model for the shallow water equations. And also the model incorporated the volume/free-surface relationship (VFR) to consider the partially submerged cells (PSC). It was identified that a simpler version of the weighted surface-depth gradient method in the MUSCL was equivalent to the original one in the accuracy for 1D steady flows. It was verified that the flux gradient term and the bottom gradient source term were well-balanced exactly by the VFR for the 1D PSC. The VFR for the triangular PSC settled the problem which the governing equations were not well-balanced by the DFB technique for the 2D PSC. There were good agreements in simulations and experiments for 2D dam-break flows over a triangular sill and a round bump. In addition, the partial dam-break flow was successfully simulated for flooding of roughnesses in an irregular bottom as well as a sloping one. Therefore, this model is expected to be applied to the real river with uneven topography.

키워드

참고문헌

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피인용 문헌

  1. Effect of Corrected Hydrostatic Pressure in Shallow-Water Flow over Large Slope vol.47, pp.12, 2014, https://doi.org/10.3741/JKWRA.2014.47.12.1177
  2. 2D Numerical Simulations for Shallow-water Flows over a Side Weir vol.48, pp.11, 2015, https://doi.org/10.3741/JKWRA.2015.48.11.957