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Numerical Methods

In Section 12-3, we showed that the unsteady flow in open channels is described by a set of hyperbolic partial differential equations. These equations describe the conservation of mass and momentum in terms of the partial derivatives of dependent variables: flow velocity, V, and flow depth, y. However, for practical applications, we need to know the value of these variables instead of the values of their derivatives. Therefore, we integrate the governing equations. Because of the presence of nonlinear terms, a closed-form solution of these equations is not available, except for very simplified cases. Therefore, they are integrated numerically for which several numerical methods have been presented.

In this chapter, we introduce the method of characteristics and discuss necessary boundary and initial conditions for the numerical solution of governing equations. Various available numerical methods are presented and their advantages and disadvantages are briefly discussed.

Keywords

Negative Characteristic Open Channel Flow Riemann Invariant Venant Equation Characteristic Grid 
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