| Abstract: | ABSTRACT The effects of the size of the Δt time step used in the integration of the implicit difference equations of unsteady open-channel flow are determined for numerous typical hydrographs with durations in the order of days or even weeks. Truncation errors related to the size of the Δt time step cause a numerical distortion (dispersion and attenuation) of the computed transient. The magnitude of the distortion is related directly to the size of the time step, the length of channel reach, and the channel resistance and inversely to the time of rise of the hydrograph. The type of finite difference expression which replaces spatial derivatives and non-derivative terms in the partial differential equations of unsteady flow has an important influence on the magnitude of the numerical distortion, as well as the numerical stability of the implicit difference equations. Time step sizes in the range of 3 to 6 hrs generally tend to minimize the combination of required computation time and numerical distortion of transients having a time of rise of the order of several days. |
