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http://dx.doi.org/10.12652/Ksce.2010.30.2B.199

Development of 2D Finite Element Model for the Analysis of Shallow Water Flow  

Seo, Il Won (서울대학교 건설환경공학부)
Song, Chang Geun (서울대학교 건설환경공학부)
Publication Information
KSCE Journal of Civil and Environmental Engineering Research / v.30, no.2B, 2010 , pp. 199-209 More about this Journal
Abstract
A finite element model for analyzing surface water flow was developed. Shallow water equation was discretized and solved by Galerkin and Newton-Raphson method. Triangular or rectangular elements can be mixed together to construct meshes. The algebraic equation was solved by frontal method which is very efficient in finite element problem. The developed model was applied to rectangular meandering channel with two bends and transverse velocities and water depth distributions were examined. High velocity was located near the inner bank at the apexes of the bends and velocity distribution was symmetrical about the centerline at the midsection of two bend and super elevation also occurred. Simulation results showed very good agreement with measured data. Another numerical simulation was carried out in mild, steep, adverse and abrupt bottom change slope and channels with weir. 12 water surface profiles of gradually varied flow were correct in terms of hydraulic interpretation.
Keywords
surface water flow; shallow water equation; finite element method; Galerkin; meandering channel; gradually varied flow;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 김승용(2002) 조위영향에 따른 신곡수중보 상하류의 유동특성 분석. 석사학위논문, 경기대학교.
2 김창완, 우효섭, 김규호, 유권규, 김 원(1995) 이차원 하천 모형의 개발 (I). 연구보고서, 95-WR-1103-1, 한국건설기술연구원.
3 김태범, 최성욱, 민경덕(2006) CDG 유한요소법을 이용한 수심적분 흐름의 수치모의, 대한토목학회논문집, 대한토목학회, 제26권 제5B호, pp. 447-457.
4 서일원, 박성원(2009) 사행수로에서 유속구조가 추적물질의 혼합에 미치는 영향, 대한토목학회논문집, 대한토목학회, 제29권 제1B호, pp. 35-45.
5 서일원, 송창근, 이명은(2008) 한강 감조구간에서의 흐름 및 혼합거동, 대한토목학회논문집, 대한토목학회, 제28권 제6B호, pp. 731-741.
6 서일원, 이규환, 백경오(2006) 사행수로의 흐름구조 및 난류특성, 대한토목학회논문집, 대한토목학회, 제26권 제5B호, pp. 469-479.
7 오정선, 서일원, 김영한(2004) 사행하천에서 오염물질의 2차원 거동특성 해석, 한국수자원학회논문집, 한국수자원학회, 제37권 제12호, pp. 979-992.   과학기술학회마을
8 윤용남, 박무종(1994) FESWMS-2DH에 의한 한강 하류부의 수리특성 분석, 대한토목학회논문집, 대한토목학회, 제14권 제4B호, pp. 847-857.
9 윤태훈(1982) 유한요소법에 의한 항만에서의 토사이동 추정모형, 대한토목학회논문집, 대한토목학회, 제2권 제2호, pp. 19-28.
10 이갑덕, 한건연, 신응배, 김정욱(1981) 수치모델에 의한 울산만내에의 수질오염도 예측, 대한토목학회 학술발표회논문집, 대한토목학회, pp. 22-24.
11 이길성, 강주환(1989) 천수방정식의 유한차분특성, 대한토목학회논문집, 대한토목학회, 제9권 제1호, pp. 41-52.
12 이진희, 김경탁, 심명필(1996) 개수로에서의 이차원 부정류 해석을 위한 유한체적법, 한국수자원학회 논문집, 한국수자원학회, 제29권 제5호, pp. 173-184.
13 최병호(1983) 경기만 남부해역의 M2 조석 영향, 대한토목학회논문집, 대한토목학회, 제3권 제2호, pp. 97-107.
14 한건연, 백창현, 박경옥(2003) SU/PG 기법에 의한 하천 흐름의 유한요소해석 : I. 이론 및 수치안정성 해석, 대한토목학회논문집, 대한토목학회, 제24권 제3B호, pp. 183-192.
15 Axelsson, O. and Barker, V.A. (1984) Finite element solution of boundary value problems. Academic Press, USA.
16 Chow, V.T. (1973) Open channel hydraulics. McGraw Hill.
17 Chung, T.J. (1992) Finite elements in fluids. Hemisphere Publishing Corporation, USA.
18 Cullen, M.P. (1976) On the use of artificial smoothing in Galerkin and finite difference solutions of the primitive equations. Quarterly Journal of the Royal Meteorological Society, Vol. 102, pp. 77-93.   DOI
19 Daily, J.W. and Harleman, D.R.F. (1966) Fluid dynamics. Addison- Wesley Publishing Company.
20 Davies, A.J. (1980) The Finite element method. Oxford University Press, New York.
21 Du Pont, T. (1973) Galerking methods for first-order hyperbolic. SIAM Journal on Numerical Analysis, Vol. 10, pp. 890-899.   DOI   ScienceOn
22 Engelman, M., Sani, R.L., and Gresho, P.M. (1982) The Implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow. International Journal for Numerical Methods in Fluids, Vol. 2, pp. 225-238.   DOI
23 Ghanem, A.H.M. (1995) Two dimensional finite element modeling of flow in aquatic habitats. Ph.D. Dissertation, University of Alberta, Edmonton, Alberta.
24 Huebner, K.H., Thornton, E.A., and Byrom, T.G. (1995) The Finite element method for engineers. John Wiley & Sons, USA.
25 Gresho, P.M. and Sani, R.L. (1998) Incompressible flow and the finite element method. John Wiley & Sons, UK.
26 Fletcher, C.A. (1984) Computational Galerkin method, Springer- Verlag, NY.
27 Heinrich, J.C. and Pepper, D.W. (1999) Intermediate finite element method. Taylor & Francis, USA.
28 Irons, B.M. (1970) A Frontal solution program for finite element analysis. International Journal for Numerical Methods in Engineering, Vol. 2, pp. 5-32.   DOI
29 Karniadakis, G.E. and Sherwin, S. (2005) Spectral/hp element methods for computational fluid dynamics. Oxford University Press, USA.
30 Kowalik, Z. and Murty, T.S. (1993) Numerical modeling of ocean dynamics. World Scientific, Singapore.
31 Navon, I.M. (1977) A survey of finite-element methods in quasi-linear fluid flow problems. WISK Report 140, National Research Institute for Mathematical Sciences. Pretoria, South Africa.
32 Oden, J.T. and Carey, F. (1982) Mathematical Aspects of the Finite Element Method. Finite element series. Vol. 4, Prentice-Hall.
33 Pepper, D.W. and Heinrich, J.C. (1992) The finite element method. Hemisphere Publishing Corporation.
34 Pinder, G.F. and Gray, W.G. (1977) Finite element simulation in surface and subsurface hydrology. Academic Press, London.
35 Praagman, N. (1982) A comparison of discretization methods for the shallow water equations. International Journal for Numerical Methods in Engineering, Vol. 18, pp. 981-995.   DOI   ScienceOn
36 Smith, I.M. (1982) Programming the finite element method. John Wiley & Sons, UK
37 Staniforth, A.N. (1987) Review: Formulating efficient finite-element codes for flows in regular domains, International Journal for Numerical Methods in Fluids, Vol. 7, pp. 1-16.   DOI   ScienceOn
38 Thomee, V. (1984) Galerkin finite element methods for parabolic problems. Springer-Verlag, Berlin.
39 Strang, G. and Fix, G.J. (1973) An analysis of the finite element method. Prentice-Hall, USA.
40 Taylor, C. and Huyakorn, P.S. (1978) A comparison of finite element based solution schemes for depicting overland flow. Applied Mathmatical Modeling, Vol. 2, pp. 185-190.   DOI   ScienceOn
41 Thomee, V. and Wendroff, B. (1974) Convergence estimates for Galerkin methods for variable coefficient initial value problems. SIAM Journal on Numerical Analysis, Vol. 11, pp. 1059-1068.   DOI   ScienceOn
42 Vreugdenhil, C.B. (1994) Numerical methods for shallow-water flow. Kluwer Aacademic Publishers, Netherlands.
43 Wait, R. and Mitchell, A.R. (1985) Finite element analysis and application. John Wiley & Sons, UK.
44 Walters, R.A. and Carey, G.F. (1983) Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations. Computer and Fluids, Vol. 11, pp. 51-68.   DOI   ScienceOn
45 Weare, T.J. (1976) Finite-element or finite-difference methods for the two dimensional shallow-water equations. Computer Methods in Applied Mechanics and Engineering, Vol. 7, pp. 351-357.   DOI   ScienceOn
46 Weiyan, T. (1992) Shallow water hydrodynamics. Elsevier, Amsterdam.