A Finite Element Model of Steady Regulated Flow in Open Channel Networks

Abstract

A numerical model of steady flow-control and profiles determination in open channel networks is developed. The model is an improvement over a previously developed hydraulic network model, in that the procedure for the solution of channel regulation by flow-control structure (gate or weir) is incorporated.The construction of the model is by a combined use of the finite element method and the Newton-Raphson iterative procedure.The basic equations to be solved are the gradually varied steady flow equations for channels, the semi-empirical stage discharge relationships for rapidly varied flow across a structure, and the energy equations for channel junctions.To ensure functional continuity that the Newton-Raphson scheme requires, the stage discharge relationships which must be altered depending on the outflow regime at the structure are assigned their respective application ranges by compatibility parameters appropriately defined.The gradually varied flow equations are directly cast into algebraic finite element equations by the standard Galerkin procedure, and then the resulting nonlinear equations are adapted into linearized recurrence form by the Newton-Raphson procedure.The channel flow equations so obtained are coupled with similarly linearized equations for structures and junctions to form the global equations system which are iteratively solved.The capability of the model is tested in terms of convergency and accuracy of the solutions to demonstrate that with rapid and stable convergency, the model improved can produce highly accurate solutions to interconnected, regulated network flow problems.