DOI QR코드

DOI QR Code

Development of 1D finite volume model for discontinues flow simulation (K-River)

불연속 흐름 모의를 위한 1차원 유한체적 모형 K-River의 개발

  • Jeong, Anchul (International Water Resources Research Institute, Chungnam National University) ;
  • An, Hyunuk (Local Environmental Engineering Department, Chungnam National University) ;
  • Kim, Yeonsu (Water Resources Research Center, K-water Convergence Institute) ;
  • Noh, Joonwoo (Water Resources Research Center, K-water Convergence Institute)
  • 정안철 (충남대학교 국제수자원연구소) ;
  • 안현욱 (충남대학교 지역환경토목학과) ;
  • 김연수 (K-water 융합연구원 물순환연구소) ;
  • 노준우 (K-water 융합연구원 물순환연구소)
  • Received : 2018.07.31
  • Accepted : 2018.09.07
  • Published : 2018.10.31

Abstract

There are a large number of weirs installed in rivers of Korea, and these characteristics are not common in other countries. When the flow passes through a structure such as a weir, discontinuous flow occurs. In terms of numerical simulation, it affects the numerical instability due to the balance between the flow term and the source term. In order to solve these problems, many researchers used empirical formulas or numerical scheme simplification. Recently, researches have been conducted to use more accurate numerical scheme. K-River was developed to reflect the characteristics of domestic rivers and calculate the discontinuous flow more accurately. For the verification of K-River, 1) numerical experiment simulations with a bump in the bed, 2) laboratory experiment of hydraulic jump simulation, 3) real river were performed. K-River verified its applicability by simulating results similar to the exact solution and observed value in all simulations.

국내의 하천에는 많은 수의 보가 설치되어 있으며, 이러한 특성은 국외에서는 흔하지 않은 편이다. 흐름이 보와 같은 구조물을 통과하는 경우에는 불연속 흐름이 발생하게 되며, 수치모의 측면에서는 흐름항과 생성항의 균형 등의 문제로 수치적 안정성에 많은 영향을 준다. 이러한 문제점을 해결하기 위해서 경험식이나 해석기법의 단순화 등에 의존해 왔으며, 최근에 들어서는 보다 정확한 수치해석기법을 이용하려는 연구가 꾸준히 수행되고 있다. K-River는 국내의 하천 특성을 반영하고, 불연속 흐름을 보다 정확히 계산하기 위한 목적으로 개발되었다. K-River의 검증을 위하여 1) 하상융기가 존재하는 개수로 수치실험 모의, 2) 도수현상 실내실험 모의, 3) 실제 하천의 수문 사상 모의를 수행하였다. 모든 모의에서 해석해 및 관측치와 유사한 결과를 모의하여 K-River의 적용성을 검증하였다.

Keywords

References

  1. Abbott, M. B., and Basco, D. R. (1989). Computational fluid dynamics. Longman Scientific and Technical, New York.
  2. Amiri, S. M., Talebbeydokhti, N., and Baghlani, A. (2013). "A two-dimensional well-balanced numerical model for shallow water equations." Scientia Iranica, Vol. 20, No. 1, pp. 97-107.
  3. An, H., and Yu, S. (2012). "Well-balanced shallow water flow simulation on quadtree cut cell grids." Advances in Water Resources, Vol. 39, pp. 60-70. https://doi.org/10.1016/j.advwatres.2012.01.003
  4. Arico, C., Sinagra, M., and Tucciarelli, T. (2013). "Anisotropic potential of velocity fields in real fluids: Application to the MAST solution of shallow water equations." Advances in Water Resources, Vol. 62, pp. 13-36. https://doi.org/10.1016/j.advwatres.2013.09.010
  5. Audusse, E., Bouchut, F., Bristeau, M. O., Klein, R., and Perthame, B. (2004). "A fast and stable well-balanced 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
  6. Chang, K.-H., Chang, T.-J., and Sheu, T. W.-H. (2017). "Development of an upwinding kernel in SPH-SWEs model for 1D transcritical open channel flows." Journal of Hydro-environment Research, Vol. 15, pp. 13-26.
  7. Cozzolino, L., and Pianese, D. (2006). "High-order finite volume modelling of one-dimensional flows." Proceedings International Conference on Fluvial Hydraulics, Taylor & Francis, Lisbon, Portugal, Vol. 1-2, pp. 493-502.
  8. Fread, D. L., Jin, M., and Lewis, J. M. (1996). "An LPI numerical implicit solution for unsteady mixed-flow simulation." Proceedings North American Water and Environment Congress, ASCE, Anaheim, CA, pp. 1-7.
  9. Goutal, N., and Maurel, F. (1997). Proceedings of the 2nd workshop on dam-break wave simulation. Technical Report HE43/97/016/A.
  10. Hu, K., Mingham, C. G., and Causon, D. M. (1998). "A bore-capturing finite volume method for open-channel flows." International Journal for Numerical Methods in Fluids, Vol. 28, No. 8, pp. 1241-1261. https://doi.org/10.1002/(SICI)1097-0363(19981130)28:8<1241::AID-FLD772>3.0.CO;2-2
  11. Jeong, A., Kim, S., Yu, W., Kim, Y., and Jung, K. (2018). "Estimation of river dredging location and volume considering flood risk variation due to riverbed change." Journal of Korean Society Hazard Mitigation, Vol. 18, No. 3, pp. 279-291. (in Korean)
  12. Jin, M., and Fread, D. L. (1997). "Dynamic flood routing with explicit and implicit numerical solution schemes." Journal of Hydraulic Engineering, Vol. 123, No. 3, pp. 166-173. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:3(166)
  13. Kim, J. S., and Han, K. Y. (2008). "One-dimensional hydraulic modeling of open channel flow using the Riemann approximate slover I: Model development." Journal of Korea Water Resources Association, Vol. 41, No. 8, pp. 761-772. (in Korean) https://doi.org/10.3741/JKWRA.2008.41.8.761
  14. Kim, J. S., Han, K. Y., and Lee, C. H. (2007). "Development of steady non-uniform flow model for a transcritical river." Journal of the Korean Society of Civil Engineers B, Vol. 27, No. 3B, pp. 219-228. (in Korean)
  15. Kim, K., Kim, J., and Kim, W. (2009). "Analysis and comparison of 1D river flow analysis model." Water for Future, Vol. 42, No. 7, pp. 56-61. (in Korean)
  16. Kim, K.-H., Lee, H.-R., and Jung, H.-R. (2016). "Improvement study of river-crossing structures in geyongnam prefecture." Journal of Korea Water Resources Association, Vol. 49, No. 10, pp. 809-821. (in Korean) https://doi.org/10.3741/JKWRA.2016.49.10.809
  17. Kim, W., Kim, J.S., and Ji, U. (2014). "Development plan of river flow numerical model." Water for Future, Vol. 47, No. 6, pp. 29-36. (in Korean)
  18. MLTMA (Ministry of Land, Transport, and Maritime Affairs) (2009). Geum river basin master plan (changed). (in Korean)
  19. Mohammed, J. R., and Qasim, J. M. (2012). "Comparison of onedimensional HEC-RAS with two-dimensional ADH for flow over trapezoidal profile weirs." Caspian Journal of Applied Sciences Research, Vol. 1, No. 6, pp. 1-12.
  20. Popescu, I. (2014). Computational hydraulics: Numerical methods and modelling. IWA Publishing.
  21. Preissmann, A. (1961). "Propagation des intumescences dans les canaux et Les Riveres." Congress de l'Association Francaise de Calcule, Grenoble, France. (in French)
  22. Rocca, M. L., Montessori, A., Prestininzi, P., and Succi, S. (2015). "A multispeed discrete Boltzmann model for transcritical 2D shallow water flows." Journal of Computational Physics, Vol. 284, pp. 117-132. https://doi.org/10.1016/j.jcp.2014.12.029
  23. Valiani, A., and Begnudelli, L. (2006). "Divergence form for bed slope source term in shallow water equations." Journal of Hydraulic Engineering, Vol. 132, No. 7, pp. 652-665. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:7(652)
  24. Wang, W., and Kelly, D. M. (2017). "A high-order PIC method for advection-dominated flow with application to shallow water waves." International Journal for Numerical Methods in Fluids, Vol. 87, pp. 583-600.
  25. Woo, H., Kim, W., and Ji, U. (2015). River hydraulics. Cheongmoongak. (in Korean)
  26. Wu, W. (2008). Computational river dynamics. Taylor & Francis, London.
  27. Zerihun, Y. T., and Fenoton, J. D. (2006). "One-dimensional simulation model for steady transcritical free surface flows at short length transitions." Advances in Water Resources, Vol. 29, No. 11, pp. 1598-1607. https://doi.org/10.1016/j.advwatres.2005.11.011
  28. Zhou, J. G., Causon, D. M., Ingram, D. M., and Mingham, C. G. (2002). "Numerical solutions of the shallow water equations with discontinuous bed topography." International Journal for Numerical Methods in Fluids, Vol. 38, No. 8, pp. 769-788. https://doi.org/10.1002/fld.243