Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Numerical Simulation of Urban Flash Flood Experiments Using Adaptive Mesh Refinement and Cut Cell Method

적응적 메쉬세분화기법과 분할격자기법을 이용한 극한 도시홍수 실험 모의

  • An, Hyun-Uk (Numerical Program Team, Division of Computational Sciences in Mathematics National Institute for Mathematical Sciences) ;
  • Yu, Soon-Young (Numerical Program Team, Division of Computational Sciences in Mathematics National Institute for Mathematical Sciences, KT Daeduk 2 Research Center)
  • 안현욱 (국가수리과학연구소 계산수리과학연구부 수치프로그램연구팀) ;
  • 유순영 (국가수리과학연구소 계산수리과학연구부 수치프로그램연구팀)
  • Received : 2011.05.30
  • Accepted : 2011.06.13
  • Published : 2011.07.31
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Abstract

Two-dimensional shallow water model based on the cut cell and the adaptive mesh refinement techniques is presented in this paper. These two mesh generation methods are combined to facilitate modeling of complex geometries. By using dynamically adaptive mesh, the model can achieve high resolution efficiently at the interface where flow changes rapidly. The HLLC Reimann solver and the MUSCL method are employed to calculate advection fluxes with numerical stability and precision. The model was applied to simulate the extreme urban flooding experiments performed by the IMPACT (Investigation of Extreme Flood Processes and Uncertainty) project. Simulation results were in good agreement with observed data, and transient flows as well as the impact of building structures on flood waves were calculated with accuracy. The cut cell method eased the model sensitivity to refinement. It can be concluded that the model is applicable to the urban flood simulation in case the effects of sewer and stormwater drainage system on flooding are relatively small like the dam brake.

적응적 메쉬세분화기법과 분할격자기법을 적용한 2차원 천수방정식모형을 활용하여 구조물을 고려한 극한 홍수 실험을 모의하였다. 본 연구에 사용된모형은 두 격자생성 기법을함께 사용함으로서 복잡한 경계를보다 적은 격자로 효율적으로 표현하는 것이 가능하며, 동적 적응 메쉬세분화기법을 사용하여 흐름이 빠르게 변하는 영역에서 정확도를 유지하면서도 효율적으로 계산하는 것이 가능하다. HLLC 리만근사해법과 MUSCL 기법을 적용하여 시공간상에서 2차정도를 유지하며, 댐붕괴파와 같은 불연속적인 흐름을 정확하게 모의할 수 있다. 모형의 검증을 위해 IMPACT 프로젝트에서 수행한 도시지역 극한홍수실험을 모의하였다. 실험결과와 모의결과가 양호하게 일치하는 것을 확인하였으며, 천이류 현상과 함께 구조물에 의한 홍수파 전달 양상이 의미있는 수준으로 모의된 것을 확인하였다. 또한 분할격자기법의 사용으로 모델의 격자 민감도가 향상되었다. 본 모델은 댐붕괴와 같이 내수침수현상이 지배적이지 않은 도시범람을 모의하는데 활용할 수 있을 것으로 기대된다.

Keywords

References

  1. 김대홍, 조용식(2004). "HLLC Approximatie Riemann Solver를 이용한 천수방정식 해석." 한국수자원학회논문집, 한국수자원학회, 제37권, 제10호, pp. 845-855. https://doi.org/10.3741/JKWRA.2004.37.10.845
  2. 김병현, 한건연, 손아롱(2011). "혼합격자의 적용이 가능한 2차원 유한체적모형의 개발." 한국수자원학회논문집, 한국수자원학회, 제44권, 제2호, pp. 109-123. https://doi.org/10.3741/JKWRA.2011.44.2.109
  3. 김형준, 김정민, 조용식(2009). "분할격자기법을 이용한 실험수조댐붕괴파의 수치모의." 대한토목학회논문집, 대한토목학회, 제29권, 제2B호, pp. 121-129.
  4. 배용훈, 고덕구, 조용식(2005). "FLUMEN 모형을 이용한 홍수범람모의." 한국수자원학회논문집, 한국수자원학회, 제38권, 제5호, pp. 355-364. https://doi.org/10.3741/JKWRA.2005.38.5.355
  5. 최승용, 김병현, 김상호, 한건연(2009). "2차 요소를 이용한 2차원 상향가중 유한요소모형." 한국수자원학회논문집, 한국수자원학회, 제42권, 제12호, pp. 1053-1067. https://doi.org/10.3741/JKWRA.2009.42.12.1053
  6. Abderrezzak, K.E.K., Paquier, A., and Mignot, E. (2009). "Modelling flash flood propagation in urban areas using a two-dimensional numerical model." Nat Hazards, Vol. 50, pp. 433-460. https://doi.org/10.1007/s11069-008-9300-0
  7. Audusse, E., Bouchut, F., Bristeau, M.O., Klein, R., and Perthame, B. (2004). "A fast and stable wellbalanced scheme with hydrostatic reconstruction for shallow water flows." SIAM Journal on Scientific Computing, Vol. 25, No. 6, pp. 2050-2065. https://doi.org/10.1137/S1064827503431090
  8. Audusse, E., and Bristeanu, M.O. (2005) "A wellbalanced positivity preserving "second-order" scheme for shallow water flows on unstructured meshes." Journal of Computational Physics, Vol. 206, pp. 311-333. https://doi.org/10.1016/j.jcp.2004.12.016
  9. Causon, D.M., Ingram, D.M., Mingham, C.G., Yang, G., and Pearson, R.V. (2000). "Calculation of shallow waterows using a Cartesian cut cell approach." Advances in Water Resources, Vol. 23, pp. 545-562. https://doi.org/10.1016/S0309-1708(99)00036-6
  10. Causon, D.M., Ingram, D.M., and Mingham, C. (2001). "A cartesian cut cell method for shallow water flows with moving boundaries." Advances in Water Resources, Vol. 24, pp. 899-911. https://doi.org/10.1016/S0309-1708(01)00010-0
  11. Griessbaum, G., and Schmidt, A. (2009). "Advanced tilt correction from flow distortion effects on turbulent $CO_2$ fluxes in complex environments using large eddy simulation." Quarterly Journal of the Royal Meteorological Society, Vol. 135, pp. 1603-1613. https://doi.org/10.1002/qj.472
  12. Harten, A. (1984). "On a class of high resolution total variation stable finite difference schemes." SIAM Journal on Numerrical Analysis, Vol. 21, No. 1, pp. 1-23. https://doi.org/10.1137/0721001
  13. Liang, Q., Borthwick, A.G.L., and Stelling, G. (2004). "Simulation of dam-and dyke-break hydrodynamics on dynamically adaptive quadtree grids." International Journal for Numerical Methods in Fluids, Vol. 46, pp. 127-162. https://doi.org/10.1002/fld.748
  14. Lopez-Herrera, J.M., Popinet, S., and Herrada, M.A. (2011). "A charge-conservative approach for simulating electrohydrodynamic two-phase flows using Volume-Of-Fluid." Journal of Computational Physics, Vol. 230, pp. 1939-1955. https://doi.org/10.1016/j.jcp.2010.11.042
  15. Mampitiyarachchi, S. (2006). "3D flow Visualisation of a micro air vehicle with winglets." Technical report, University of Sydney, October, http://gfs.sf.net/papers/mampiti2006.pdf.
  16. Roe, P.L. (1981). "Approximate riemann solvers, parameter vectors and difference schemes." Journal of Computational Physics, Vol. 43, pp. 357-372. https://doi.org/10.1016/0021-9991(81)90128-5
  17. Rogers, B., Fujihara, M., and Borthwick, A.G.L. (2001). "Adaptive Q-tree Godunov-type scheme for shallow water equations." International Journal for Numerical Methods in Fluids, Vol. 35, pp. 247-280. https://doi.org/10.1002/1097-0363(20010215)35:3<247::AID-FLD89>3.0.CO;2-E
  18. Rogers, B.D., Borthwick, A.G.L., and Taylor, P.H. (2003) "Mathematical balancing of ux gradient and source terms prior to using Roe's approximate Riemann solver." Journal of Computational Physics, Vol. 192, No. 2, pp. 422-451. https://doi.org/10.1016/j.jcp.2003.07.020
  19. Popinet, S. (2003). "Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries." Journal of Computational Physics, Vol. 190, No. 2, pp. 572-600. https://doi.org/10.1016/S0021-9991(03)00298-5
  20. Popinet, S., and Rickard, G. (2007). "A tree-based solver for adaptive ocean modelling." Ocean Modelling, Vol. 16, pp. 224-249. https://doi.org/10.1016/j.ocemod.2006.10.002
  21. Popinet, S., Gorman, R.M., Rickard, G.J., and Tolman, H.L. (2010). "A quadtree-adaptive spectral wave model." Ocean Modelling, Vol. 34, pp. 36-49. https://doi.org/10.1016/j.ocemod.2010.04.003
  22. Popinet, S. (2011a) "Quadtree-adaptive tsunami modelling." Ocean Dynamics, accepted.
  23. Popinet, S. (2011b). "River vertex test modelling." http://gfs.sourceforge.net/wiki/index.php/RiverVortexest.
  24. Quirk, J.J. (1994). "An alternative to unstructed grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies." Journal of Computers and Fluids, Vol. 23, pp. 125-142. https://doi.org/10.1016/0045-7930(94)90031-0
  25. Soares Frazao, S., Noël, B., Spinewine, B., and Zech, Y. (2003). "Flood propagation-The isolated building test case-Results from the benchmark. In EC Contract EVG1-CT-2001-00037 IMPACT Investigation of Extreme Flood Processes and Uncertainty." Proceedings 3rd Project Workshop, Louvain-la-Neuve, Belgium 6-7 November 2003 (CD-ROM).
  26. Testa, G., Zuccala, D., Alcrudo, F., Mulet, J., and Soares Frazao, S. (2007). "Flash flood flow experiment in a simplified urban district." Journal of Hydraulic Research, Vol. 45, Extra Issue, pp. 37-44. https://doi.org/10.1080/00221686.2007.9521831
  27. Toro, E.F., Spruce, M., and Speares, W. (1994). "Restoration of the contact surface in the HLL Riemann solver," Shock Waves, Vol. 4, pp. 25-34. https://doi.org/10.1007/BF01414629
  28. van Leer, B. (1984). "On the relation between the upwinddifferencing schemes of Godunov, Engquist-Osher and Roe." SIAM Journal on Scientific and statistical Computing, Vol. 5, pp. 1-20. https://doi.org/10.1137/0905001

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