DOI QR코드

DOI QR Code

Numerical analysis of dam breaking problem using SPH

제체의 갑작스런 붕괴로 인한 충격파 수치해석 - SPH (Smoothed Particle Hydrodynamics)를 중심으로

  • 조용준 (서울시립대학교 토목공학과) ;
  • 김권수 (서울시립대학교 대학원 토목공학과)
  • Received : 2007.12.17
  • Accepted : 2008.03.23
  • Published : 2008.05.31

Abstract

Even though there is a great deal of progress in a numerical method of high caliber like SPH, it is very rarely deployed in a water resources community. Despite the great stride in computing environment, depth averaged approach like a nonlinear shallow equation is still efficient tool for flood routing in large watershed, but it can give some misleading information like the inundation height of flood. In this rationale, we numerically simulate the flow into the dry channel, dry channel with an obstacle triggered by the collapse of a two dimensional water column using SPH (Smoothed Particle Hydrodynamics) in order to boost the application of numerical method of high caliber like SPH in a water resources community. As a most severe test of the robustness of SPH, we also carry out the simulation of the flow through a clearance into the wet channel driven by the rapid removal of a water gate. As a hydrodynamic model, we used the Navier-Stokes equation, a numerical integration of which was carried out using SPH. To verify the validity of newly proposed numerical model, we compare the numerically simulated flow with the others in the literature mainly from VOF and MAC, and hydraulic experiments by Martin and Moyce (1952), Koshizuka et al. (1995) and Janosi et al. (2004). It was shown that agreements between the numerical results in this study and hydraulic experiments are remarkable.

최근 진행된 정밀 수치해석 기법의 비약적인 발전에도 불구하고 SPH 등과 같은 고급수치기법의 수자원 분야에서의 활용은 그리 활발해 보이지 않는다. 대규모 수계를 대상으로 한 flood routing의 경우 비선형 천수방정식으로 대표되는 depth averaged approach가 효과적이나 정밀한 범람고 예단에는 오류가 야기될 수 있다. 본 고에서는 SPH 수치해석 기법의 수자원 분야로의 적용가능성을 모색하기 위해 비교적 수리모형실험자료가 풍부한 제체붕괴로 인한 수리현상을 수치모의하였다 (Martin과 Moyce, 1952). 보다 완벽한 검증을 위해 수로에 장애물이 거치된 경우 (Koshizuka 등, 1995), 수문의 갑작스런 개방으로 인한 수로에서의 수리현상 (Janosi 등, 2004) 등 점진적으로 난이도를 높여 수치모의를 수행하였다. 동수역학 모형 방정식으로는 Navier-Stokes 방정식, 동수역학의 수치적 적분에는 Smoothed Particle Hydrodynamics 기법을 채택하였다. 모의 결과 본 고에서의 수치모의가 기존에 선호되던 VOF, MAC의 수치 기법에 비해 우월한 결과를 보였다.

Keywords

References

  1. 조용준, 이 헌(2007) Lagrangian Dynamic Smagorinsky 난류모 형과 SPH를 이용한 쇄파역에서의 비선형천수거동에 관한 연 구. 한국해안해양공학회지, 한국해안해양공학회, Vol. 19, No. 1, pp. 81-96
  2. 조용준, 김권수, 유하상(2008) Swash 대역에서의 해빈표사 부유 거동에 관한 연구, 대한토목학회논문집, 대한토목학회, 제28권 제1B호, pp. 95-109
  3. Batchelor, G.K. (1967) An Introduction to fluid dynamics. Cambridge Univ. Press, Cambridge, UK
  4. Crespo, A.J.C., Gomez-Gesteira, M., and Dalrymple, R.A. (2007). 3D SPH simulation of large waves mitigation with a dike. J. of Hydraulic Research, Vol. 45, No. 5, pp. 631-642 https://doi.org/10.1080/00221686.2007.9521799
  5. Dalrymple, R.A., Knio, O. (2000) SPH Modeling of water waves. Proc. Coastal Dynm., Lund 2000
  6. Dalrymple, R.A., and Rogers, B.D. (2006) Numerical modeling of water waves with the SPH method. Coastal Engineering, Vol. 53, pp. 141-147 https://doi.org/10.1016/j.coastaleng.2005.10.004
  7. Gingold, R.A. and Monaghan, J.J. (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astr. Soc. Vol. 181, pp. 375-389 https://doi.org/10.1093/mnras/181.3.375
  8. Gomez-Gesteira, M., cerqueiro, D., Crespo, C., and Dalrymple, R. A. (2005) Green water overtopping analyzed with a SPH model. Ocean Engineering, Vol. 32, pp. 223-238 https://doi.org/10.1016/j.oceaneng.2004.08.003
  9. Hirt, C.W. and Nichols, B.D. (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput Phys, Vol. 39, pp. 201-225 https://doi.org/10.1016/0021-9991(81)90145-5
  10. Janosi, I.M., Jan, D., Szabo, K.G., and Tel, T. (2004) Turbulent Drag Reduction in Dam-Break Flows. Experim. Fluid Vol. 37, pp. 219-229 https://doi.org/10.1007/s00348-004-0804-4
  11. Koshizuka, S., Tamako, H., and Oka, Y. (1995) A particle method for incompressible viscous flow with fluid fragmentation. Comput. Fluid. Dynamics J., Vol. 4, pp. 29-46
  12. Lin, P.Z. and Liu Philip, L.F. (1998) A numerical study of breaking waves in the surf zone. J. Fluid Mech., Vol. 359, pp. 239-264 https://doi.org/10.1017/S002211209700846X
  13. Lucy, L.B. (1977) A Numerical approach to testing the fusion hypothesis. Astronomical Journal, Vol. 82, pp. 1013-1024 https://doi.org/10.1086/112164
  14. Martin, J.C. and Moyce, W.J. (1952) An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philosophical Transactions of the Royal Society of London, Series A, Vol. 244, pp. 312-324 https://doi.org/10.1098/rsta.1952.0006
  15. Meneveau, C., Lund, T. S., and Cabot, W. H. (1996) A Lagrangian dynamic subgrid-scale model of turbulence. Journal of Fluid Mech., Vol. 319, pp. 353-385 https://doi.org/10.1017/S0022112096007379
  16. Monaghan, J.J. (1987) SPH meets the Shocks of Noh. Monash University Paper
  17. Monaghan, J.J. (1992) Smoothed particle hydrodynamics. Ann. Rev. Astronomy and Astrophysics, Vol. 30, pp. 543-574 https://doi.org/10.1146/annurev.aa.30.090192.002551
  18. Monaghan J.J. (1994) Simulating free surface flows with SPH. Journal of Computational Physics, Vol. 110, pp. 399-406 https://doi.org/10.1006/jcph.1994.1034
  19. Monaghan, J.J. and Gingold, R.A. (1983) Shock simulation by the particle method of SPH. Journal of Computational Physics, Vol. 52, pp. 374-381 https://doi.org/10.1016/0021-9991(83)90036-0
  20. Monaghan, J.J. and Kos, A. (1999) Solitary waves on a Cretan beach. J. of Waterway, Port, Coastal and Ocean Engineering, Vol. 125, pp. 145-154 https://doi.org/10.1061/(ASCE)0733-950X(1999)125:3(145)
  21. Monaghan, J.J. and Kos, A. (2000) Scott Russell's wave generator. Phys. Fluids, Vol. 12, pp. 622-630 https://doi.org/10.1063/1.870269
  22. Monaghan, J.J. and Poinracic, J. (1985) Artificial viscosity for particle methods. applied Numerical Mathematics, Vol. 1, pp. 187-194 https://doi.org/10.1016/0168-9274(85)90015-7
  23. Morris, J.P., Fox, P.j., and Zhu, Y. (1997) Modeling low Reynolds number incompressible flow using SPH. Journal of Computational Physics Vol. 136, pp. 214-226 https://doi.org/10.1006/jcph.1997.5776
  24. Pan, C.H., Xu, X.Z., and Lin, B.Y. (1993) Simulating free surface flows by MAC method. Estuar Coastal Eng, Vol. 1-2, pp. 51- 58 (in Chinese)
  25. Pope, Stephen B. (2000) Turbulent flows. Cambridge Univ. Press, Cambridge, UK
  26. Pope, Stephen B. (2004) Ten questions concerning the large-eddy simulation of turbulent flows. New Journal of Physics, Vol. 6, No. 35, pp. 1-24 https://doi.org/10.1088/1367-2630/6/1/001
  27. Rodi, Wolfgang (1993) Turbulence models and their application in hydraulics - a state of art review. International Association for Hydraulic Research, Delft, 3rd edition 1993, Balkema
  28. Shao, S. and Lo, Edmond Y.M. (2003) Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Advances in Water Resources 26, pp. 787-800 https://doi.org/10.1016/S0309-1708(03)00030-7
  29. Smagorinsky, J. (1963) General circulation experiments with the primitive equations, I. the Basic Experiment. Monthly Weather Review, Vol. 91, pp. 99-164 https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
  30. Takeda, H., Shoken, M.M., and Minoru, Sekiya (1994) Numerical simulation of viscous flow by smoothed particle hydrodynamics. Progress in Theoretical Physics 92, pp. 939-959
  31. Ubbink, O. (1997) Numerical prediction of two fluid systems with sharp interfaces. Ph. D. Thesis, Imperial College of Science, Technology and Medicine, London
  32. Yoshizawa, A. (1986) Statistical theory for compressible turbulent shear flows with application to sub-grid modeling. Physics of Fluids A 29, pp. 2152-2164 https://doi.org/10.1063/1.865552