DOI QR코드

DOI QR Code

A Novel Scheme to Depth-averaged Model for Analyzing Shallow-water Flows over Discontinuous Topography

불연속 지형을 지나는 천수 흐름의 해석을 위한 수심적분 모형에 대한 새로운 기법

  • Received : 2015.11.02
  • Accepted : 2015.11.10
  • Published : 2015.12.01

Abstract

A novel technique was proposed to calculate fluxes accurately by separation of flow area into a part of step face which is dominated by flow resistance of it and an upper part which is relatively less affected by the step face in analyzing shallow-water flows over discontinuous topography. This technique gives fairly good agreement with exact solutions, 3D simulations, and experimental results. It has been possible to directly analyze shallow-water flows over discontinuous topography by the technique developed in this study. It is expected to apply the developed technique to accurate evaluation of overflows over weirs or retaining walls (riverside roads) and areas flooded by the inundation in the city covered in discontinuous topography.

불연속 지형을 지나는 천수 흐름의 해석에서 흐름률을 정확하게 계산하기 위하여 계단에 의한 흐름 저항이 지배적인 계단 전면과 그 영향이 비교적 덜한 계단의 윗부분을 구분하여 접근하는 새로운 기법을 제안하였다. 새로운 기법에 의한 모의 결과는 정확해, 가상의 문제에 대한 3차원 모의 결과, 그리고 실험 결과와 대체로 잘 일치하였다. 이 연구에서 개발된 기법으로 불연속 하천구조물을 넘나드는 천수 흐름에 대한 직접 해석이 가능해졌다. 보나 옹벽(강변 도로)의 월류 양상 그리고 불연속 지형으로 이루어진 도심에서 범람에 따른 침수 구역의 정확한 산정에 개발된 기법의 적용이 기대된다.

Keywords

References

  1. Alcrudo, F. and Benkhaldoun, F. (2001). "Exact solutions to the Riemann problem of the shallow water equations with a bottom step." Comput. & Fluids, Vol. 30, pp. 643-671. https://doi.org/10.1016/S0045-7930(01)00013-5
  2. Batten, P., Lambert, C. and Causon, D. M. (1996). "Positively conservative high-resolution convection schemes for unstructured elements." Int. J. Numer. Meth. Eng., Vol. 39, pp. 1821-1838. https://doi.org/10.1002/(SICI)1097-0207(19960615)39:11<1821::AID-NME929>3.0.CO;2-E
  3. Bermudez, A. and Vazquez, M. E. (1994). "Upwind methods for hyperbolic conservation laws with source terms." Comput. & Fluids, Vol. 23, pp. 1049-1071. https://doi.org/10.1016/0045-7930(94)90004-3
  4. Chow, V.T. (1959). Open-channel hydraulics, McGraw Hill Co., Inc.
  5. Gusev, A. V., Ostapenko, V. V., Malysheva, A. A. and Malysheva, I. A. (2008). "Open-channel waves generated by propagation of a discontinuous wave over a bottom step." J. Appl. Mech. Tech. Phys., Vol. 49, pp. 23-33. https://doi.org/10.1007/s10808-008-0004-8
  6. 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
  7. Hwang, S. Y. (2013a). "Finite-volume model for shallow-water flow over uneven bottom." J. KWRA, Vol. 46, pp. 139-153 (in Korean).
  8. Hwang, S. Y. (2013b). "Exact and approximate Riemann solvers for the shallow-water flows over a step." Proc. KWRA Conf., KWRA, p. 575 (in Korean).
  9. Hwang, S. Y. (2013c). "Exact solutions of the Riemann problem for the shallow-water flow over a step to the dry-bed." Proc. 39th KSCE Conf., KSCE, pp. 1515-1518 (in Korean).
  10. Hwang, S. Y. (2014). "A study on imposing exact solutions as internal boundary conditions in simulating the shallow-water flows over a step." J. KSCE, Vol. 34, pp. 479-492 (in Korean). https://doi.org/10.12652/Ksce.2014.34.2.0479
  11. Hwang, S. Y. (2015). "2D numerical simulations for shallow-water flows over discontinuous topography." Proc. 41th KSCE Conf., KSCE (in Korean; publishing).
  12. Hwang, S. Y. and Lee, S. H. (2012). "An application of the HLLL approximate Riemann solver to the shallow water equations." J. KSCE, Vol. 32, pp. 21-27 (in Korean).
  13. LeVeque, R. J. (2002). Finite volume method for hyperbolic problems, Cambridge Univ. Press.
  14. Linde, T. (2002). "A practical, general-purpose, two-state HLL Riemann solver for hyperbolic conservation laws." Int. J. Numer. Meth. Fluids, Vol. 40, pp. 391-402. https://doi.org/10.1002/fld.312
  15. Prokof'ev, V. A. (2005). "Two-dimensional horizontal numerical model of open flow over a bed with obstacles." Water Resources, Vol. 32, No. 3, pp. 252-264. https://doi.org/10.1007/s11268-005-0034-z
  16. Weiyan, T. (1992). Shallow water hydrodynamics, Elsevier Science Publishers.
  17. 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." Int. J. Numer. Meth. Fluids, Vol. 38, pp. 769-788. https://doi.org/10.1002/fld.243
  18. 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-water equations." J. Comput. Phys., Vol. 168, pp. 1-25. https://doi.org/10.1006/jcph.2000.6670