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http://dx.doi.org/10.3741/JKWRA.2003.36.5.777

Weighted Averaged Flux Method for Computation of Shallow Water Equations  

Kim, Woo-Gu (한국수자원공사 수자원연구원)
Jung, Kwan-Sue (충남대학교 공과대학 토목공학과)
Kim, Jae-Han (충남대학교 공과대학 토목공학과)
Publication Information
Journal of Korea Water Resources Association / v.36, no.5, 2003 , pp. 777-785 More about this Journal
Abstract
A numerical model for the solution of two-dimensional free surface flow is developed on unstructured grid. By using fractional step method, the two-dimensional shallow water equations (SWE) are treated as two one-dimensional problems. Thus, it is possible to simulate computational hydraulic problems with higher computational efficiency. The one-dimensional problems are solved using upwind TVD version of second-order Weighted Averaged Flux (WAF) scheme with HLLC approximate Riemann solver. The numerical oscillations which are common with second-order numerical scheme are controlled by exploiting WAF flux limiter, Some idealized test problems are solved using this model and very accurate and stable solutions are obtained. It can be concluded as an efficient implement for the computation of SWE including dam break problems that concerning discontinuities, subcritical and supercritical flows and complex domain.
Keywords
WAF method; HLLC Riemann solver; TVD scheme; Shallow water equations; Wet and Dry technique;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Brocchini, M., Bernetti, R, Mancinelli, A, and Albertini, G. (2001). 'An efficient solver for nearshore flows based on the WAF method.' Coastal Engineering, Vol. 43, pp. 105-129   DOI   ScienceOn
2 Kim, D. H., Kim, W. G., Chae, H. S. and Park, S. G. (2002). 'Development of 2D Dam Break Flow Analysis Model using Fractional Step Method.' Water Engineering Research, Vol. 3, No. 1, pp. 23-30
3 Zhao, D.H., Shen, H.W., Tabios III, G.Q., Lai, J.S., and Tan, W.Y. (1994), 'A finite volume two-dimensional unsteady flow model for river basins,' J. of Hydraulic Engineering, ASCE, Vol. 120, No. 7, pp. 863-883   DOI   ScienceOn
4 Zoppou, C., Stephen, R. (1999), 'Catastrophic collapse of water supply reservoirs in urban areas,' J. of Hydraulic Engineering, ASCE, Vol. 125, No. 7, pp. 686-695   DOI
5 김원 (1999). '고정확도 수치기법을 이용한 하천 천이류 해석모형의 개발.' 박사학위논문, 경북대학교
6 Zoppou, C., and Stephen, R. (2000), 'Numerical solution of two-dimensional unsteady dam break.' Applied Mathematical Modelling, Vol. 24, pp. 457-475   DOI   ScienceOn
7 강민구, 박승우 (2003). 'ENO 기법을 이용한 2차원 유한체적 수치모형.' 한국수자원학회논문집, 36권, 1호, pp. 1-13   과학기술학회마을   DOI
8 이성태 (1998). '이차원 수리 충격파 모의를 위한 유한체적 비정상 흐름 모형.' 석사학위논문, 서울대학교
9 Beffa, C., and Connell, R.J. (2001). 'Two dimensional flood plain flow. I : model description.' J. of Hydrologic Engineering, Vol. 6, No. 5, pp. 397-405   DOI   ScienceOn
10 Fraccarollo, L., and Toro, E.F. (1995). 'Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems.' J. of Hydraulic Research, Vol. 33, No. 6, pp. 843-864   DOI   ScienceOn
11 Weiyan, T. (1992), Shallow water hydrodynamics, Elsevier
12 Bellos, C. V., Soulis, J. V., and Sakkas. J. G. (1992). 'Experimental investigation of two-dimensional dam-break induced flows.' J. of Hydraulic Reserch, Vol. 30, No. 1, pp. 47-63   DOI
13 Billett, S. J., and Toro, E. F. (1997). 'On WAF-Type Schemes for Multidimensional Hyperbolic Conservation Laws.' J. of Computational Physics, Vol. 130, No. 1, pp. 1-24   DOI   ScienceOn
14 Bradford, S.F., and Sanders, B.F. (2002). 'Finite-volume model for shallow-water flooding of arbitrary topography.' J. of Hydraulic Engineering, Vol. 128, No. 3, pp. 289-298   DOI   ScienceOn
15 Glaister, P. (1988). 'Approximate Riemann solutions of the shallow water equations.' J. of Hydraulic Research, 26, No. 3, pp. 293-306   DOI
16 Liggett, J. A. (1994). Fluid mechanics, McGraw-Hill
17 Thacker, W. C. (1981). 'Some exact solutions to the nonlinear shallow water wave equations.' J. of Fluid Mechanics, Vol. 107, pp. 499-508   DOI   ScienceOn
18 Mingham, C.G., and Causon, D.M. (1999). 'Calculation of unsteady bore diffraction using a high resolution finite volume method.' J. of Hydraulic Research, Vol. 38, No. 1, pp. 49-56
19 Wang, J.S., Ni, H.G., and He, Y.S. (2000). 'Finite-difference TVD scheme for Computation of dam-break problems.' J, of Hydraulic Engineering, Vol. 126, No. 4, pp. 253-262   DOI   ScienceOn
20 Zhao, D.H., Shen, H.W., Lai, J.S., and Tabios III, G.T. (1996). 'Approximate Riemann solvers in FVM for 2d hydraulic shock wave modeling.' J. of Hydraulic Engineering, ASCE, Vol. 122, No. 12, pp. 692-702   DOI   ScienceOn