Accurate Diffusive Wave Routing

Abstract

The diffusive wave simplification of the unsteady, open-channel flow equations is a commonly used approach for flood routing applications. Among the many routing methods, except for those based on the De Saint-Venant equations, it may be considered to be the one that most closely complies with the physics of open-channel hydraulics. However, common implementations of the diffusive wave approach (linear diffusion, variable parameter diffusion) involve additional approximations that diminish its physical significance and accuracy. A new formulation for the nonlinear diffusive wave is presented that better respects conservation principles through close consistency with the fundamental flow equations. The accuracy and reliability of the proposed model are shown on test cases consisting both of a hypothetical, regular channel, and of an actual river reach. Simulated discharges are compared to those obtained by a full De Saint-Venant model and by ordinary diffusion methods, as well as to observed hydrographs in the real-world test case. This model, based on hydraulic theory, can be safely applied to a wide range of flow conditions, while complying with the practical constraints of flow routing applications, including the usual nonavailability of adequate channel geometry data.