Abstract
This study deals with practical and reliable method to calculate interior boundary conditions. Interior boundary conditions are compatibility conditions connecting two subcritical flows between which a supercritical flow or a hydraulic structure exists. The Preissmann scheme, an implicit finite difference scheme, is widely used for an open channel unsteady flow calculation because of no restrictions on Δx and Δt. Interior boundary conditions, which are essential for the Preissmann scheme to calculate a partially supercritical flow, are sometimes very complex. In such a case, it is difficult for the ordinary Newton-Raphson method to obtain a convergent solution.
In this study, four interior boundary conditions corresponding to typical hydraulic structures were used. The mechanism of non-convergency was analyzed and means were then sought to improve numerical convergency. For this purpose, a smooth curve was used to replace a complex discharge equation in interior boundary conditions, and several relaxation rates in the Newton-Raphson iteration procedure were applied. These means in combination were more effective for improving stability and convergency without reducing accuracy.
