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Selection of ?x and ?t Computational Steps for Four-Point Implicit Nonlinear Dynamic Routing Models

by D. L. Fread, Natl Weather Service, Silver Spring, United States,
J. M. Lewis, Natl Weather Service, Silver Spring, United States,



Document Type: Proceeding Paper

Part of: Hydraulic Engineering

Abstract:

A major step in a successful application of unsteady flow models based on the numerical (four-point implicit, nonlinear finite-difference) solution of the complete one -dimensional Saint-Venant equations, is the selection of the magnitudes of the computational distance step (? x) and time step (? t) used in the numerical solution technique. A theoretical explanation is presented for the basis of the empirical selection criteria used rather successfully for a number of years; also, an enhanced time step selection criterion is presented. The suitability of the selection criteria is demonstrated using a numerical convergence testing technique for a wide spectrum of unsteady flow applications ranging from rapidly to slowly rising hydrographs in very flat to very steep sloping channels.

Subject Headings: Numerical methods | Dynamic models | Finite difference method | Unsteady flow | Numerical models | Hydraulic models | Approximation methods

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