FLOOD ROUTING BASED ON DIFFUSION WAVE-EQUATION USING MIXING CELL METHOD

A one-dimensional non-linear diffusion wave equation is derived from t he 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 conve rt the differential equation to difference form. In this study, the mi xing cell method is used to convert the diffusion wave equation to dif ference form, in which the difference term can be eliminated by select ing an optimal space step size Delta x when time step size Delta t is given. When the time step size Delta t --> 0, the space step size Delt a x = Q/(2S(0)BC(k)) where Q is discharge, S-0 is bed slope, B is chan nel width and C-k is kinematic wave celerity, which is the same as the characteristic length proposed by Kalinin and Milyukov. The results o f application to two cases show that the mixing cell and linear channe l how routing methods produce hydrographs that are in agreement with t he observed flood hydrographs. (C) 1997 John Wiley & Sons, Ltd.