한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제44권3호
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  • Pages.249-262
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  • 2011
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  • 2799-8746(pISSN)
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  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
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2차원 유한체적모형을 이용한 댐 붕괴파 모의에 관한 연구

A Study on Simulation of Dam-break Wave Using Two-dimensional Finite Volume Model

  • 정우창 (경남대학교 공과대학 토목공학과) ;
  • 박영진 (서일대학 토목공학과)
  • 투고 : 2011.01.13
  • 심사 : 2011.03.16
  • 발행 : 2011.03.31
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초록

본 연구에서는 댐 붕괴파와 같이 연속 및 불연속 흐름해석에 적용되고 있는 HLLC 기법을 불규칙한 하상지형에서의 흐름해석에 적용할 때 생성항과 흐름률항의 사이의 수치적 불균형으로 인한 수치진동을 감소시키기 위해 well-balanced HLLC 기법과 천수방정식에 근거한 비구조적 유한체적모형을 개발하였으며, 이를 댐 붕괴파 문제에 적용하였다. 적용된 well-balanced HLLC 기법은 단순히 흐름률항을 계산할 때 하상지형경사를 직접 포함시키는 것으로 정상상태의 천이류에 적용하였을 때 생성항과 흐름률항 사이에 수치적 균형이 이루어짐을 확인하였다. 수치모형의 검증을 위해 댐 붕괴파 문제와 관련된 세 가지 서로 다른 수리모형실험과 프랑스 Mapasset 댐 붕괴에 대한 현장사례에 적용하였으며, 적용결과 본 연구에서 개발된 모형은 수리모형실험 그리고 현장에서 관측된 결과와 비교적 잘 일치하는 것으로 나타났으며, 기존의 모형으로부터 계산된 모의결과에 비해 비교적 정확한 결과를 나타내었다.

In this study, in order to reduce the numerical oscillation due to the unbalance between source and flux terms as the HLLC scheme is applied to the flow analysis on the irregular bed topography, a unstructured finite volume model based on the well-balanced HLLC scheme and the shallow water equations is developed and applied to problems of dam-break waves. The well-balanced HLLC scheme considers directly the gradient of bed topography as the flux terms is calculated. This scheme provides the good numerical balance between the source and flux terms in the case of the application to the steady-state transcritical flow. To verify the numerical model developed in this study, it is applied to three cases of hydraulic model experiments and a field case study of Mapasset dam failure (France). As a result of the verification, the predicted numerical results agree relatively well with available laboratory and field measurements. The model provides slightly more accurate results compared with the existing models.

키워드

참고문헌

  1. 김대홍, 조용식 (2005). “불규칙 지형에 적용가능한 쌍곡선형 천수방정식을 위한 개선표면경사법”. 대한토목학회논문집, 대한토목학회, 제25권, 제3B호, pp. 223-229.
  2. 김병현, 한건연, 안기홍 (2009). “Riemann 해법을 이용한 댐 붕괴파의 전파 해석”, 대한토목학회 논문집, 대한토목학회, 제29권, 제5B호, pp. 429-439.
  3. 김형준 (2008). Numerical Simulation of Shallow-Water Flow Using Cut-Cell System, 박사학위논문, 한양대학교, pp. 1-142.
  4. Anastasiou, K., and Chan, C.T. (1997). “Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes.” International Journal for Numerical Methods in Fluid, Vol. 16, pp. 489–505.
  5. Billett, S.J., and Toro, E.F. (1997), “On WAF-type schemes for multi-dimensional hyperbolic conservation laws.” Journal of Computational Physics, Vol. 130, No.1, pp. 1-24. https://doi.org/10.1006/jcph.1996.5470
  6. Brufau, P., and Garcia-Navarro, P. (2003), “Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique.” Journal of Computational Physics, Vol. 186, pp. 503-526. https://doi.org/10.1016/S0021-9991(03)00072-X
  7. Brufau, P., Vazquez-Cendon, M.E., and Garcia-Navarro, P. (2002), “A Numerical model for the flooding and drying of irregular domains.” International Journal for Numerical Methods in Fluids, Vol. 39, pp. 247-275. https://doi.org/10.1002/fld.285
  8. Guo, W.D., Lai, J.S., and Lin, G.F. (2007). “Hybrid fluxsplitting Finite Volume schemes for shallow-water flow simulations with source term.” Journal of Mechanics, Vol. 23, No. 4, pp. 399-414. https://doi.org/10.1017/S1727719100001453
  9. Harten, A. Lax, P., and van Leer, A. (1983). “On upstream differencing and Godunov-type scheme for hyperbolic conservation laws.” Society for Industrial and Applied Mathematics, Review, Vol. 25, No. 1, pp. 35-61.
  10. Hervouet, J.M., and Petitjean, A. (1991). “Malpasset dam break revisited with two-dimensional computations.” Journal of Hydraulic Research, Vol. 37, No. 6, pp. 777-788.
  11. Honnorat (2007), Assimilation de donnees lagrangiennes pour la simulation numerique en hydraulique fluvial, Ph.D. Thesis, Institut National Polytechnique de Grenoble, France, pp. 1-144.
  12. Leveque, R.L., and George, D.L. (2004). “High-resolution finite volume methods for the shallow water equations with bathymetry and dry states.” Proceedings of the Third International Workshop on Long-Wave Runup Models, Advances in Coastal and Ocean Engineering, Catalina, Vol. 10, pp. 43-73.
  13. Loukili, Y., and Soulaïmani, A. (2007). “Numerical Tracking of Shallow Water Waves by the Unstructured Finite Volume WAF Approximation.” InternationalJournal for Computational Methods in Engineering Science and Mechanics, Vol. 8, pp. 1-14. https://doi.org/10.1080/15502280601006140
  14. Perthame, B., and Simeoni, C. (2001). “A kinetic scheme for the Saint-Venant extended Kalman Filter for data assimiliation in oceanography.” Calcolo, Vol. 38, No. 4, pp. 201-231. https://doi.org/10.1007/s10092-001-8181-3
  15. Sleigh, P.A., Gaskell, P.H., Berzins, M., and Wright, N.G. (1998). “An unstructured finite-volume algorithm for predicting flow in rivers and estuaries.” Computational Fluids, Vol. 27, No. 4, pp. 479-508. https://doi.org/10.1016/S0045-7930(97)00071-6
  16. Soares-Frazao S., and Zech Y. (1999). “Effects of a sharp bend on dam-break flow”, Proceedings 28th IAHR Congress, Graz, Austria, published on CD-ROM, pp. 1-20.
  17. Toro, E.F. (2001). Shock-capturing methods for freesurfaceshallow flows. Wiley, New York. pp. 1-309.
  18. Valiani, A., Caleffi, V., and Zanni, A. (2002). “Case Study: Malpasset Dam-Break Simulation Using a Two-Dimensional Finite Volume Method.” Journal ofHydraulic Engineering, ASCE, Vol. 128, No. 5, pp. 460-472. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:5(460)
  19. Yoon, T.H., and Kang, S.K. (2004). “Finite volume model for two-dimensional shallow water flows on unstructured grids.” Journal of Hydraulic Engineering,ASCE, Vol. 130, No. 7, pp. 678-688. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:7(678)
  20. Zhao, D.H., Shen, H.W., Tabios, G.Q., Lai, J.S., and Tan, W.Y. (1996), “Finite-volume two-dimensional unsteadyflow model for river basins.” Journal of Hydraulic Engineering, ASCE, Vol. 120, No. 7, pp. 863-883.
  21. Zhou, J.G., Causon, D.M., Mingham, C.G., and Ingram,D.M. (2001). “The surface gradient method for the treatment of source terms in the shallow-waterequation.” Journal of Computational Physics, Vol. 168, pp. 1-25. https://doi.org/10.1006/jcph.2000.6670
  22. Zhou, J.G., Causon, D.M., Mingham, C.G., and Ingram, D.M. (2004). “Numerical Prediction of dam-break flows in general geometries with complex bed topography.” Journal of Hydraulic Engineering, ASCE, Vol. 130, No. 4, pp. 332-340. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:4(332)
  23. Zoppou, C., and Roberts, S. (2003). “Explicit schemes for dam-break simulations.” Journal of Hydraulic Engineering, ASCE, Vol. 129, No. 1, pp. 11-34. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:1(11)

피인용 문헌

  1. Hydraulic Characteristics of Dam Break Flow by Flow Resistance Stresses and Initial Depths vol.47, pp.11, 2014, https://doi.org/10.3741/JKWRA.2014.47.11.1077
  2. A Study on Simulation of Dam-Break Wave Using a Three-Dimensional Numerical Model vol.12, pp.2, 2012, https://doi.org/10.9798/KOSHAM.2012.12.2.181