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Numerical Analysis of Dam-Break Flow in an Experimental Channel using Cut-Cell Method

분할격자기법을 이용한 실험수조 댐붕괴파의 수치모의

  • 김형준 (한양대학교 대학원 건설환경공학과) ;
  • 김정민 (한양대학교 대학원 건설환경공학과) ;
  • 조용식 (한양대학교 건설환경공학과)
  • Received : 2008.07.25
  • Accepted : 2008.12.01
  • Published : 2009.03.31

Abstract

In this study, dam-break flows are simulated numerically by using an efficient and accurate Cartesian cut-cell mesh system. In the system, most of the computational domain is discretized by the Cartesian mesh, while peculiar grids are done by a cutcell mesh system. The governing equations are then solved by the finite volume method. An HLLC approximate Riemann solver and TVD-WAF method are employed to calculation of advection flux of the shallow-water equations. To validate the numerical model, the model is applied to some problems such as a steady flow convergence on an ideal bed, a steady flow over an irregular bathymetry, and a rectangular tank problem. The present model is finally applied to a simulation of dam-break flow on an experimental channel. The predicted water surface elevations are compared with available laboratory measurements. A very reasonable agreement is observed.

본 연구는 효율적이며 정확한 격자생성기법인 분할격자기법을 이용하여 댐붕괴 흐름을 수치모의한다. 분할격자기법은 부분적으로 비구조격자를 사용하지만, 대부분의 흐름영역을 균일한 크기의 Cartesian 격자로 이산화한다. HLLC Riemann 근사해법과 TVD-WAF기법의 유한체적기법을 적용하여 흐름률을 계산하고 분할격자의 영역을 위한 수치모형을 구성한다. 수치모형을 검증하기 위하여 이상적인 하도에서의 정상류, 불균일하도에 의해 형성되는 정상류 및 사각형수조의 자유진동흐름을 모의하여 해석해와 비교하였다. 마지막으로, 실험수로에서 발생한 댐붕괴파의 흐름을 모의하여 관측값과 비교하여 정확하고 안정된 결과를 확인하였다.

Keywords

References

  1. 김대홍, 조용식(2005) 불규칙 지형에 적용가능한 쌍곡선형 천수방정식을 위한 개선표면경사법, 대한토목학회논문집, 대한토목학회, 제25권, 제3B호 pp. 223-229.
  2. 이정규, 김태관(2003) 댐붕괴 문제의 해석에 관한 TVD-McCormack기법의 적용, 한국수자원학회논문집, 한국수자원학회, 제36권, 제3호, pp. 365-374. https://doi.org/10.3741/JKWRA.2003.36.3.365
  3. 이종욱, 조용식(2001) TVD수치모형의 개발 : 천수방정식, 한국수자원학회논문집, 한국수자원학회, 제34권, pp. 187-195.
  4. 인태훈, 박구용, 조용식(2003) Quadtree격자를 이용한 근해지진해일의 처오름높이 계산, 한국수자원학회논문집, 한국수자원학회, 제36권, pp. 705-713. https://doi.org/10.3741/JKWRA.2003.36.4.705
  5. 한건연, 박재홍(1995) 도시하천에서의 홍수범람도 작성을 위한 2차원 모형의 개발, 한국수자원학회논문집, 한국수자원학회, 제28권, 제6호, pp. 119-131.
  6. 한건연, 김동구, 이홍래(1999) McCormack 기법을 이용한 하천흐름의 동수역학 해석, 한국수자원학회 학술발표회 논문집, 한국수자원학회, pp. 590-595.
  7. Berger, M.J., Helzel, C., and Leveque, R.J. (2003) h-Box methods for the approximation of hyperbolic conservation laws on irregular grids, SIAM J. Numer. Anal., Vol. 41, pp. 893-918. https://doi.org/10.1137/S0036142902405394
  8. Billet, S.J. and Toro, E.F. (1997) On the accuracy and stability of explicit schemes for multidimensional linear homogeneous advection equations. J. Computational Physics, Vol. 131, No. 4, pp. 247-250. https://doi.org/10.1006/jcph.1996.5610
  9. Causon, D.M., Ingram, D.M., and Mingham, C.G. (2001) A cartesian cut cell method for shallow water flows with moving boundaries. Adv. Water Resour., Vol. 24, pp. 899-911. https://doi.org/10.1016/S0309-1708(01)00010-0
  10. Causon, D.M., Ingram, D.M., Mingham, C.G., Yang, G., and Pearson, R.V. (2000) Calculation of shallow water flows using a Cartesiancut cell approach. Adv. Water Resour., Vol. 23, pp. 545-562. https://doi.org/10.1016/S0309-1708(99)00036-6
  11. Fraccarollo, L. and Toro, E.F. (1995) Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems. J. Hydr. Res. Vol. 33, pp. 843-864. https://doi.org/10.1080/00221689509498555
  12. Gao, F., Ingram, D.M., Causon, D.M., and Mingham, C.G. (2006) The development of a Cartesian cut cell method for incompressible viscous flows. Int. Journal for Numerical method in fluids, Vol. 54, pp. 1033-1053.
  13. Glaister, P. (1988) An approximate linearised Riemann solver for the Euler equations of gas dynamics. J. Computational Physics, Vol. 74, pp. 382-408. https://doi.org/10.1016/0021-9991(88)90084-8
  14. Goutal, N. and Maurel, F. (1997) HE-43/97/016B. Proceedings of the 2nd workshop on dam-break wave simulation:Department Laboratoire National d’Hydraulic, Groupe Hydraulic Fluviale Electricite de Fracne, France.
  15. Ingram, D.M., Causon, D.M., and Mingham, C.G. (2003) Development in Cartesian cut cell methods. Math. and Computers in simulation, Vol. 61, pp. 561-572. https://doi.org/10.1016/S0378-4754(02)00107-6
  16. Kim, J. and Choi, H. (2004) An Immersed-boundary finite volume method for simulation of heat transfer in complex geometries, KSME, International J., Vol. 18, pp. 1026-1035.
  17. Liang, Q., Borthwick, A.G.L., and Stelling, G. (2004) Simulatoin of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids, International Journal of Numerical Method in Fluids, Vol. 46, pp. 127-162. https://doi.org/10.1002/fld.748
  18. Loukili, Y. and Soulaeimani, A. (2007) Numerical tracking of shallow water waves by the unstructured finite volume WAF approximation. International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 8, pp. 75-88. https://doi.org/10.1080/15502280601149577
  19. Lynch, D.R. and Gray, W.G. (1978) Analytic solutions for computer flow model testing. J. the Hydraulic Division, ASCE, Vol. 104, No. HY10, pp. 1409-1428.
  20. Morris, M. (2000) CADAM: Concerted action on dambreak modeling-Final report. Rep. No. SR 571, HR Wallingford.
  21. Park, K.Y. (1999) Quadtree grid numerical model of nearshore wave-current interaction, Ph. D. thesis, Oxford Univ., U. K.
  22. Peskin, C.S. (1982) The fluid dynamics of heart valves: experimental, theoretical, and computational methods, Annual Review of Fluid Mechanics, Vol. 14, pp. 235-259. https://doi.org/10.1146/annurev.fl.14.010182.001315
  23. Toro, E.F. (2001) Shock-capturing method for free-surface shallow flows. Wiley.
  24. Qian, L., Causon, D.M., Ingram, D.M., and Mingham, C.G. (2003) Cartesian cut cell two-fuid solver for hydraulic flow problems. J. Hydr. Engineering. Vol. 129, pp. 688-696. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:9(688)
  25. Qian, L., Causon, D.M., Ingram, D.M., Mingham, C.G., and Zhou, J.G. (2001) A Cartesian cut cell method for incompressible viscous flows. Proc., European Community on Computational Methods in Applied Sciences (ECCOMAS), CFD 2001, Institute of Mathematics and its Applications, Southend-on Sea, U.K.
  26. Younus, M. and Chaudhry, M.H. (1994) A depth-averaged k-e turbulence model for the computation of free-surface flow. J. Hydr. Res., Vol. 32, pp. 415-444. https://doi.org/10.1080/00221689409498744
  27. 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. Hydr. Engineering, Vol. 130, No. 4, pp. 332-340. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:4(332)