Analysis of a Diffusion Wave Flow Routing Model with Application to Flow in Waters,
Ferrick,M. G.
Bilmes,J.
Long,S. E.
A one-dimensional diffusion wave flow routing model, modified for tailwaters, simulates the important physical processes affecting the flow and is straightforward to apply. The model is based upon a numerical solution of the kinematic wave equation. The modified equation, Hirt, and von Neumann analyses are used to gain insight into the stability and dissipative and dispersive behavior of the numerical solution, and results of these analyses are compared. A set of linear routings is used to demonstrate the dissipative and dispersive behavior predicted by the analyses and to verify the accuracy of an expression that quantifies the numerical diffusion of the model. The analyses provide a basis for selection of numerical parameters for model applications. The capability and accuracy of the model are enhanced when physical wave diffusion is balanced by numerical diffusion in the model. Maintaining the diffusion balance requires that the time derivative weighting parameter theta be variable and in some instances negative. Though some amount of phase error is introduced, negative theta values have no adverse effect upon model stability. Field studies were conducted to demonstrate the benefits of careful model development and analysis, and to verify the diffusion wave model for rapidly varying tailwater flow. The bed slope and roughness characteristics of the field study reaches below Appalachia and Norris Dams differ greatly, spanning those of a large number of rivers of practical interest. The accurate simulation of flow in both of these tailwaters attests to the soundness of both the physical basis of the model and the numerical solution technique.