Adaptation of Preissmann's scheme for transcritical open channel flows

Despite being widely used for the solution of one-dimensional subcritical flows governed by Saint-Venant's equations, the Preissmann's scheme cannot solve transcritical flows. This inability is due only to the solution methods created for non-transcritical flows. Transcritical transitions present specific properties that have to be adequately represented in the numerical method. A modified version of Preissmann's method is presented herein that changes the formulation only in transcritical zones, while keeping its conservative property and shock capturing form otherwise. A solution method is proposed for the implicit system, through storing the transcritical positions. This enables to solve the system with simple and double-sweep methods. The transcritical transition problem is solved locally, either by associating the cells involved in a bore and adding an equation to characterize the information transferred into the subcritical domain, or by the addition of an internal boundary condition to characterize the expansion fan at the critical point.