Adaptation of Preissmann’s scheme for transcritical open channel flows

Despite 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 which have to be adequately represented in the numerical method. A modified version of Preissmann’s method is presented herein which 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 in the subcritical domain, or by the addition of an internal boundary condition to characterize the expansion fan at the critical point. RÉSUMÉ Bien qu'il soit fréquemment utilisé pour la résolution des écoulements 1D fluviaux régis par les équations de Saint-Venant, le schéma de Preissmann ne peut pas traiter les écoulements transcritiques. Cette incapacité est uniquement due aux méthodes de résolution généralement utilisées, car elles ont été mises au point pour les écoulements non transcritiques. Ces transitions présentent des caractéristiques particulières qui doivent être correctement gérées par la méthode numérique employée. Une version modifiée du schéma Authorproduced version of the article published in Journal of Hydraulic Research, 2010, 48(4), 428-440. The original publication is available at http://www.tandfonline.com/ doi : 10.1080/00221686.2010.491648