Flow routing is a mathematical method (model) to predict the changing magnitude, speed, and shape of a flood wave at one or more locations along waterways such as rivers, reservoirs, canals, or estuaries. The flood wave can emanate from precipitation runoff (rainfall or snowmelt), reservoir releases (spillway flows or dam failures), and tides (astronomical and/or wind generated).

Flow routing has long been of vital concern and many ways have been developed to predict the characteristic features of a flood wave to improve the transport of water through natural or man-made waterways and to determine necessary actions to protect life and property from the effects of flooding. Commencing with investigations by Newton (1687), Laplace (1776), Poisson (1816), Boussinesq (1871), and culminating in the one-dimensional equations of unsteady flow derived by Barré de Saint-Venant (1871), the theoretical foundation for flow routing was essentially achieved. The original Saint-Venant equations are the conservation of mass equation:

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