DOI QR코드

DOI QR Code

Application of Channel Routing Model by Taylor-Galerkin Finite Element Method -Modeling of Flow in Flood-

테일러-갤러킨 유한요소법에 의한 하도추적 모형의 적용 -홍수시 하천 유량 모의-

  • 이해균 (단국대학교 천안캠퍼스 토목환경공학과)
  • Received : 2010.11.03
  • Accepted : 2010.12.22
  • Published : 2011.01.28

Abstract

For the simulation of one-dimensional unsteady flow, the Taylor-Galerkin finite element method was adopted to the discretization of the Saint Venant equation. The model was applied to the backwater problem in a single channel and the flood routing in dendritic channel networks. The numerical solutions were compared with previously published results of finite difference and finite element methods and good agreement was observed. The model solves the continuity and the momentum equations in a sequential manner and this leads to easy implementation. Since the final system of matrix is tri-diagonal with a few additional entry due to channel junctions, the tri-diagonal matrix solution algorithm can be used with minor modification. So it is fast and economical in terms of memory for storing matrices.

Acknowledgement

Supported by : 단국대학교

References

  1. 한건연, 백창현, 박경옥, "SU/PG 기법에 의한 하천흐름의 유한요소 해석 - I. 이론 및 수치안정성 해석". 대한토목학회논문집, 대한토목학회, 제24권, 제IIIB호, pp.183-192, 2004a.
  2. 한건연, 박경옥, 백창현. "SU/PG 기법에 의한 하천흐름의 유한요소 해석 - II. 적용". 대한토목학회논문집, 대한토목학회, 제24권, 제IIIB호, pp.193-199, 2004b.
  3. Chaudhry, M.H. Open-Channel Flow, Springer, 2007.
  4. G. W. Choi and A. Molinas, "Simultaneous solution algorithm for channel network modeling.” Water Resource Research, Vol.29, pp.321-328, 1993. https://doi.org/10.1029/92WR01949
  5. J. A. Cunge, F. M. Holly, Jr. and A. Verwey, Practical Aspects of Computational River Hydraulics. Pitman Press, 1980.
  6. J. Donea, "A Taylor-Galerkin method for convective transport problems," International Journal for Numerical Methods in Engineering, Vol.20. pp.101-120, 1984. https://doi.org/10.1002/nme.1620200108
  7. F. E. Hicks and P. M. Steffler, "A Characteristic-Dissipative-Galerkin scheme for open channel flow" Journal of Hydraulic Engineering, ASCE, Vol.118, No.2, pp.337-352, 1992. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:2(337)
  8. T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications, 2000.
  9. N. Katopodes, "Two-dimensional surges and shocks in open channels". Journal of Hydraulic Engineering, ASCE, Vol.110, No.6, pp.794-812, 1984. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:6(794)
  10. N. Katopodes and C. T. Wu, "Explicit computation of discontinuous channel flow," Journal of Hydraulic Engineering, ASCE, Vol.112, No.6, pp.456-475, 1986. https://doi.org/10.1061/(ASCE)0733-9429(1986)112:6(456)
  11. J. Peraire, O. C. Zienkiewicz, and K. Morgan, "Shallow water problems: a general explicit formulation," International Journal for Numerical Methods in Engineering, Vol.22, pp.547–574, 1986.
  12. Y. Zhang, “Simulation of open channel network flows using finite element approach,” Communications in Nonlinear Science and Numerical Simulation, Vol.10, pp.467-478, 2005. https://doi.org/10.1016/j.cnsns.2003.12.006