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

摘要

The purpose of this report is to document the stream-network visualization andschematization, flow-governing equations, and solution procedures used in the FEQ model to simulate 1-D unsteady flow in a network of open channels and control structures. The basic principles of 1-D unsteady-flow modeling and the relation between steady flow and unsteady flow are discussed to give readers who are familiar with steady-flow analysis points of reference for understanding unsteady-flow analysis. The schematization of the stream system and the conversion of the physical characteristics of the stream reaches, including the effects of curvilinearity, into function tables for model applications are described. The modified dynamic-wave equation used in FEQ is developed for unsteady flow in curvilinear channels with drag forces on minor hydraulic structures and channel constrictions determined from an equivalent energy slope. The equations approximating flow through various hydraulic-control structures are presented, and conversions of the stage-discharge relations for these structures into function tables are given. The matrix equation relating flows and depths at computational nodes throughout the river system by the continuity (conservation of mass) and modified dynamic-wave equations is illustrated for four sequential examples. The solution of the matrix equation by Newton's method is discussed. Finally, the input for FEQ and the error messages and warnings issued in model simulation are listed.