ABSTRACT
This chapter discusses some of the more useful methods after briefly introduces solution techniques. Using hydraulic methods for unsteady-flows, the unsteady continuity equation and momentum equation are solved simultaneously. One solution technique used to solve the unsteady-flow equation is the method of characteristics, developed to solve hyperbolic partial differential equations. A significant number of numerical schemes have been proposed to solve the one-dimensional, unsteady-flow equations. Three general methods include: the method of characteristics, finite-difference methods, and finite-element methods. The properties of the kinematic wave allow an exact solution for the simple case where there are no lateral inflows. The numerical solution techniques discussed above all require specification of initial conditions and conditions at the model boundaries. Predicting and describing the effects of unsteady- flows using dynamic-flow models can be critical in many studies of water quality.
