Numerical treatment of a discontinuous top surface in 2D shallow water mixed flow modeling

This paper presents a numerical strategy based on shallow water equations (SWE) coupled with the 2D Preissmann slot model to handle a ceiling step discontinuity in finite volume schemes for mixed flow modeling. In practice, a typical situation would be a closed structure, such as a bridge or culvert, which induces a sudden vertical flow constriction and may even run partly or totally full in high flow conditions. In such case, both the inlet and outlet of the structure involve a discontinuity in the top elevation. This special singularity is topologically represented by inserting a fictitious cell between 2 adjacent computational cells characterized by sharply different ceiling elevation. The 2D SWE are solved by means of a well-balanced quasi-conservative Godunov-type numerical scheme based on the Slope Limiter Centered (SLIC) scheme. The flow variables at each boundary of the fictitious cell are reconstructed by adopting the cross-sectional shape of the adjoining cell. Accordingly, the dynamic effect of the structure deck on the flow is suitably modeled, and the C-property for a stationary solution is rigorously satisfied, even when the closed structure is partially full. The capability of the numerical scheme is verified by comparison with both novel analytical solutions of 1D Riemann problems with a ceiling step discontinuity and experimental data of steady and unsteady mixed flows available in literature. Finally, a real-scale application to a multiple arch bridge is presented. The results show that the method is robust and effective in predicting the 2D features induced by a crossing structure on the flow dynamics.