COMPARISON OF SPECTRAL AND FINITE-DIFFERENCE METHODS FOR FLOOD ROUTING

This investigation presents a spectral method for solving the one-dime nsional shallow-water wave equations. The spectral method is based on the Chebyshev collocation technique and finite-difference time steppin g. The spectral method and finite-difference Preissmann scheme are app lied to route a log-Pearson Type III hydrograph through a wide rectang ular channel, and the results are compared. The spectral method perfor ms better than the Preissmann scheme as long as the time-stepping erro rs are kept low. However, for larger time steps, the Preissmann scheme , which is almost second-order accurate in time (and second-order accu rate in space) performs better than the spectral scheme, which is firs t-order accurate in time and has so-called infinite-order accuracy in space. This seems to indicate that the order of accuracy in time discr etization is more important than that in space discretization? in nume rical models, for fast-rising floods and friction-dominated flows.