Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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2-D SU/PG Finite Element Model Using Quadratic Elements

2차 요소를 이용한 2차원 상향가중 유한요소모형

  • Choi, Seung-Yong (School of Archi. & Civil Engineering, Kyungpook National Univ.) ;
  • Kim, Byung-Hyun (School of Archi. & Civil Engineering, Kyungpook National Univ.) ;
  • Kim, Sang-Ho (Department of Civil Engineering, Sangji Univ.) ;
  • Han, Kun-Yeun (School of Archi. & Civil Engineering, Kyungpook National Univ.)
  • 최승용 (경북대학교 공과대학 건축.토목공학부) ;
  • 김병현 (경북대학교 공과대학 건축.토목공학부 BK21사업단) ;
  • 김상호 (상지대학교 이공과대학 건설시스템공학과) ;
  • 한건연 (경북대학교 공과대학 건축.토목공학부)
  • Published : 2009.12.31
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Abstract

The objective of this study is to develop an efficient and accurate quadratic finite element model based on Streamline Upwind/Petrov Galerkin (SU/PG) scheme for analyzing and predicting two dimensional flow features in complex natural rivers. For a development of model, quadratic tin, quadrilateral and mixed elements as well as linear tin, quadrilateral and mixed elements were used in the model. Also, this model was developed through reinforcement of Gauss Quadrature which was necessary to integral of governing equation. Several tests for bottom-rising channel and U-type channel were performed for the purpose of validation and verification of the developed model. Such results showed that solutions of second order elements are better accurate and improved than those of linear elements. Results obtained by the developed model and RMA-2 model are compared, and the results for the developed model were better accurate than those of RMA-2 model. In the future if the developed model is applied in natural rivers, it can provide better accurate results than those of existing model.

본 연구의 목적은 하도의 형상이 불규칙한 자연하천에서 2차원 흐름 특성을 해석하고 예측하기 위해 2차 요소를 이용한 정확하고 효과적인 상향가중 유한요소모형의 개발에 있다. 모형의 개발을 위해 선형 삼각형 요소, 선형 사각형 요소와 혼합요소를 적용하였고 2차 삼각형, 사각형 요소와 혼합요소를 적용하여 모형을 개발하였으며, 지배방정식의 수치적분식으로 Gauss Quadrature 방법을 사용하였다. 개발된 모형의 적용성 검증을 위해 하상융기가 있는 수로, U자형 수로 등에 모의를 실시하여 해석해 및 실측치와 비교 검토하였다. 모의 결과 2차 요소가 선형 요소에 비해 보다 정확한 해를 제공하는 것으로 판단되었으며 2차요소를 적용한 상용모형인 RMA-2 모형과 비교한 결과 본 연구 개발 모형이 보다 정확한 해를 나타내는 것을 확인할 수 있었다. 개발된 모형을 향후 자연하천에 적용할 경우 기존의 모형에 비해 향상된 결과를 얻을 수 있을 것으로 판단된다.

Keywords

References

  1. 백창현 (2006). 하천흐름해석을 위한 3차원 상향가중 유한요소모형의 개발. 박사학위논문, 경북대학교, pp. 6-11
  2. 윤용남, 박무종 (1994). “FESWMS-2DH에 의한 한강 하류부의 수리특성 분석.” 대한토목학회논문집, 제14권, 제4호 pp. 847-857
  3. 윤태훈 (1982). “유한요소법에 의한 항만에서의 토사이동 추정모형.” 대한토목학회논문집, 제2권, 제2호, pp. 847-857
  4. 한건연, 김상호 (2000). “Petrov-Galerkin 기법에 의한 하천에서의 이송-확산 해석.” 대한토목학회논문집, 제20권, 제2-B호, pp. 45-53
  5. 한건연, 박경옥, 백창현 (2003). “SU/PG 기법에 의한 하천흐름의 유한요소해석 : II. 적용.” 대한토목학회논문집, 제24권, 제3B호, pp. 193-199
  6. 한건연, 이종태, 박재홍 (1996). “개수로내의 점변 및 급변 부정류에 대한 유한요소해석: I. 이론 및 수치안정성 해석.” 한국수자원학회논문집, 제29권, 제4호, pp. 167-178
  7. Alam, M.M. and Bhuiyan, M.A. (1995). “Collocation finite element simulation of dam-break flows.” Journal of Hydraulics. Engineering, ASCE, Vol. 121, No. 2, pp. 118-128 https://doi.org/10.1061/(ASCE)0733-9429(1995)121:2(118)
  8. Allaire, P.E. (1985). Basis of the finite element method, Ph.D. dissertation, University of Virginia, pp. 8-24
  9. Bell, S.W., Elliot, R.C. and Chaudhry, M.H. (1992). “Experimental results of two-dimensional dam-break flows.” Journal of Hydraulics Research Vol. 30, No. 2, pp. 225-252 https://doi.org/10.1080/00221689209498936
  10. Berger, R.C. (1993). A Finite Element Scheme Shock Capturing, Technical Report HL-93-12, pp. 1-8
  11. Berger, R.C. and Howington, S.E. (2005). “Discrete Fluxes and Mass Balances in Finite Elements.” Journal of Hydraulics Engineering, Vol. 128, pp. 97-92 https://doi.org/10.1061/(ASCE)0733-9429(2002)128:1(87)
  12. Daubert, A. and Graffe, O. (1967). Quelques aspects des ecoulements presque horizontaux a deux dimensions en plan non permants application aux estuaires,. La Houille Blanche, No. 8, pp. 847-860 https://doi.org/10.1051/lhb/1967059
  13. Dupont, T. (1973). “Galerkin methods for first-order hyperbolics : An example.” SIAM Journal of Numerical Analysis, Vol. 10, pp. 890-899 https://doi.org/10.1137/0710074
  14. Gee, D.M. and MacArthur, R.C. (1981). “Evaluation and Application of the Generalized Finite Element Hydrodynamics Model, RMA-2.” Two-Dimensional Modeling, Hydrologic Engineering Center, pp. 97-113
  15. Goutal, N. and Maurel, F. (1997). “High resolution schemes for hyperbolic conservation laws.” Journal of Computational Physics, Vol. 49, No.3, pp. 357-393
  16. Gray, W.G. (1980). “Do Finite Element Models Simulate Surface Flow?” Finite Elements in Water Resources III, Univ. of Mississippi Press, pp. 122-136
  17. Hicks, F.E. and Steffler, P.M. (1992). “Characteristic dissipative Galerkin scheme for open channel flow.” J. of Hyd. Eng., ASCE, Vol. 118, No. 2, pp. 337-352 https://doi.org/10.1061/(ASCE)0733-9429(1992)118:2(337)
  18. Katopodes, N.D. (1984). “A dissipative Galerkin scheme for open-channel flow.” Journal of Hydraulics Engineering, ASCE, Vol. 110, No. 4, pp. 450-466 https://doi.org/10.1061/(ASCE)0733-9429(1984)110:4(450)
  19. King, I.P. and Norton, W.R. (1978). “Recent application of RMA's finite element models for two-dimensional hydrodynamics and water quality.” Finite Element in Water Resources, Pentech Press, pp. 81-99
  20. Lee, J.K. and Froehlich, D.C. (1986). Review of Literature on the Finite Element Solution of the Equations of Two-Dimensional Flow in the Horizontal Plane, U. S. Geological Survey Circular 1009, pp. 1-65
  21. Norton, W.R. (1980). “EBMUD Hydrodynamic and Water Quality Models for San Francisco Bay.” Resources Management Associates, pp. 1-260
  22. Stockstill, R.L. and Berger, R.C. (1994). A Two- Dimensional Flow Model for High-Velocity Channels, Technical Report REMR-HY-12, pp. 1-11
  23. Van Rijn, L.C. (1990). Aqua Publications, Amsterdam, The Netherlands, pp. 5-35
  24. Walters R.A. (1983). “Numerically induced oscillations in finite element approximations to shallow water equations.” International Journal for Numerical Methods in Fluids, Vol. 3, pp. 591-604 https://doi.org/10.1002/fld.1650030606
  25. Walters, R.A. and Cheng, R.T. (1978). “A Two-Dimensional Hydrodynamic Model of a Tidal Estuary.” Finite Elements in Water Resources, Pentech, pp. 3-21
  26. Weiyan, T. (1992). Shallow water hydrodynamics, Elsevier Oceanography Series, pp. 1-37
  27. Zienkiewicz, O.C. and Codina, R. (1996). “A general algorithm for compressible and incompressible flow-Part I. The split, characteristic based scheme.” International Journal for Numerical Methods in Fluids, Vol. 20, pp. 869-885 https://doi.org/10.1002/fld.1650200812
  28. Zienkiewicz, O.C., Nithiarasu, P., Codina, R. and Vazquez, M. (1999). “The characteristic based split procedure: An efficient and accurate algorithm for fluid problems.” International. Journal for Numerical Methods in Fluids, Vol. 31, pp. 359-392 https://doi.org/10.1002/(SICI)1097-0363(19990915)31:1<359::AID-FLD984>3.0.CO;2-7

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