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Warianty tytułu
Języki publikacji
Abstrakty
In this paper, the conservative properties of the Muskingum equation, commonly applied to solve river flood routing, are analysed. The aim of this analysis is to explain the causes of the mass balance error, which is observed in the numerical solutions of its non-linear form. The linear Muskingum model has been considered as a semi-discrete form of the kinematic wave equation and therefore it was possible to derive its two non-linear forms. Both forms were derived directly from the kinematic wave equation. It appeared that depending on the assumed conservative form of the Muskingum equation, this model satisfies either the global mass conservation law or the global momentum conservation law. Both laws are satisfied simultaneously by the linear equation only. The mass balance error can be eliminated from the numerical solution on condition that the non-linear Muskingum equation is written in the proper conservative form.
Rocznik
Tom
Strony
121--137
Opis fizyczny
Bibliogr. 17 poz., il.
Twórcy
autor
- Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233 Gdańsk, Poland, gadar@pg.gda.pl
Bibliografia
- 1. Chow V. T., Maidment D. R. and Mays L. W. (1988) Applied Hydrology, McGraw-Hill International Editors.
- 2. Cunge J. A. (1969) On the subject of a flood propagation computation method (Muskingum method). Journal of Hydraulic Research, 7 (2), 205–230.
- 3. Cunge J. A., Holly F. M. and Verwey A. (1980) Practical Aspects of Computational River Hydraulics, Pitman, London.
- 4. Fletcher C. A. (1991) Computational Techniques for Fluid Dynamics, Vol. I, Springer Verlag, Berlin.
- 5. Gasiorowski D. and Szymkiewicz R. (2007) Mass and momentum conservation in the simplified flood routing models, Journal of Hydrology, 346, 51–58.
- 6. Gresho P. M. and Sani R. L. (1998) Incompressible Flow and the Finite-Element Method, Volume 1: Advection-Diffusion, John Wiley, Chichester.
- 7. Lai C., Baltzer R. A. and Schafranek R. W. (2002) Conservation form equation of unsteady open-channel flow, Journal of Hydraulic Research, 40 (5), 567–578.
- 8. LeVeque R. J. (2002) Finite Volume Methods for Hyperbolic Problems, Cambridge University Press.
- 9. Miller W. A. and Cunge J. A. (1975) Simplified equations of unsteady flow. In: Miller, W. A. and Yevjewich, V. (Editors) Unsteady Flow in Open Channels, Water Resources Publishing, Fort Collins.
- 10. Mohan S. (1997) Parameter estimation of non-linear Muskingum models using genetic algorithm, Journal of Hydraulic Engineering ASCE, 123 (2), 137–142.
- 11. Ponce V. M. and Chaganti P. V. (1994) Muskingum-Cunge method revised, Journal of Hydrology, 163, 433–439.
- 12. Ponce V. M. and Yevjevich V. (1978) Muskingum-Cunge methods with variable parameters, Journal of the Hydraulics Division ASCE, 104 (9), 1663–1667.
- 13. Szymkiewicz R. (2002) An alternative IUH for hydrological lumped models, Journal of Hydrology, 259, 246–253.
- 14. Tang X., Knight D. W. and Samuels P. G. (1999a) Volume conservation characteristics of the variable parameter Muskingum-Cunge method for flood routing, Journal of Hydraulic Engineering ASCE, 125 (6), 610–620.
- 15. Tang X., Knight D. W. and Samuels P. G. (1999b) Variable parameter Muskingum-Cunge method for flood routing in a compound channel, Journal of Hydraulics Research, 37 (5), 591–614.
- 16. Toro E. F. (1997) Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, Berlin.
- 17. Tung Y. K. (1984) River flood routing by non-linear Muskingum method, Journal of Hydraulics Division ASCE, 111 (9), 1447–1460.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BATA-0009-0092