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Flood routing based on diffusion wave equation using mixing cell method
Author(s) -
Singh V. P.,
Wang GuangTe,
Adrian D. D.
Publication year - 1997
Publication title -
hydrological processes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.222
H-Index - 161
eISSN - 1099-1085
pISSN - 0885-6087
DOI - 10.1002/(sici)1099-1085(199711)11:14<1881::aid-hyp536>3.0.co;2-k
Subject(s) - hydrograph , discretization , mathematics , mixing (physics) , flow (mathematics) , mathematical analysis , differential equation , channel (broadcasting) , routing (electronic design automation) , physics , geometry , flood myth , computer science , computer network , quantum mechanics , philosophy , theology
A one‐dimensional non‐linear diffusion wave equation is derived from the Saint Venant equations with neglect of the inertia terms. This non‐linear equation has no general analytical solution. Numerical schemes are therefore employed to discretize the space and time axes and convert the differential equation to difference form. In this study, the mixing cell method is used to convert the diffusion wave equation to difference form, in which the difference term can be eliminated by selecting an optimal space step size Δ x when time step size Δ t is given. When the time step size Δ t →0, the space step size Δ x = Q /(2 S 0 BC ] k ) where Q is discharge, S 0 is bed slope, B is channel width and C k is kinematic wave celerity, which is the same as the characteristic length proposed by Kalinin and Milyukov. The results of application to two cases show that the mixing cell and linear channel flow routing methods produce hydrographs that are in agreement with the observed flood hydrographs. © 1997 John Wiley & Sons, Ltd.