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Full Equations (FEQ) Model for the Solution of the Full, Dynamic Equations of Motion for One-Dimensional Unsteady Flow in Open Channels and Through Control Structures

U.S. GEOLOGICAL SURVEY WATER-RESOURCES INVESTIGATIONS REPORT 96-4240

6. APPROXIMATION OF THE FULL EQUATIONS OF MOTION IN A BRANCH

The integral form of the full equations of motion representing flow in a branch, derived previously, must be converted to an approximate algebraic form for numerical solution. Approximate solutions must be obtained by applying numerical methods because exact solutions of the equations are limited to a few special cases. The following sections describe the numerical methods available for solution of the approximated integral equations of motion, and the four options available in FEQ for approximating the equations of motion. General rules are given for approximate integration by weighted algebraic computation of the flow and water-surface elevation derivatives with respect to time and space. The approximations of the equations of motion are developed for the most general of the four approximation options. Finally, the selection of the appropriate weights for the time and distance integrals are discussed with respect to the selected approximation option in FEQ.

6.1 Methods of Mathematical Approximation
6.2 Equations of Motion Options
6.3 Rules for Approximate Integration
6.4 Conservation of Mass
6.5 Conservation of Momentum
6.6 Selection of Weights
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