Problem of Head-Discharge Relationships in 6-Point Staggered Schemes

Abstract

The 6-point staggered scheme has inherent problems with the schematization of hydraulic processes that are described by head-discharge relationships in the form of (1) rating relationships specifying downstream boundary conditions; and (2) local hydraulic processes governed by a range of energy and mass conservation equations, e.g., weir and sluice equations. There are methods to get around these problems, but they require the staggering of head and discharge in the local reach of the system. These methods are therefore liable to introduce uncertainties into their modeling. The presented numerical scheme overcomes these uncertainties. The scheme has an accuracy that is second order, as opposed to first order traditional approaches. Additionally, it imposes no further assumptions and employs head-discharge relationships in their familiar standard format.