Extension and application of the Preissmann slot model to 2D transient mixed flows

This paper presents an extension of the Preissmann slot concept for the modeling of highly transient two-dimensional (2D) mixed flows. The classic conservative formulation of the 2D shallow water equations for free surface flows is adapted by assuming that two fictitious vertical slots, aligned along the two Cartesian plane directions and normally intersecting, are added on the ceiling of each integration element. Accordingly, transitions between free surface and pressurized flow can be handled in a natural and straightforward way by using the same set of governing equations. The opportunity of coupling free surface and pressurized flows is actually useful not only in one-dimensional (1D) problems concerning sewer systems but also for modeling 2D flooding phenomena in which the pressurization of bridges, culverts, or other crossing hydraulic structures can be expected. Numerical simulations are performed by using a shock-capturing MUSCL-Hancock finite volume scheme combined with the FORCE (First-Order Centred) solver for the evaluation of the numerical fluxes. The validation of the mathematical model is accomplished on the basis of both exact solutions of 1D discontinuous initial value problems and reference radial solutions of idealized test cases with cylindrical symmetry. Furthermore, the capability of the model to deal with practical field-scale applications is assessed by simulating the transit of a bore under an arch bridge. Numerical results show that the proposed model is suitable for the prediction of highly transient 2D mixed flows