Extension of the two‐component pressure approach for modeling mixed free‐surface‐pressurized flows with the two‐dimensional shallow water equations

Abstract

Numerical models based on the two‐dimensional shallow water equations (2D‐SWE) are routinely used in flood risk management and inundation studies. However, most of these models do not adequately account for vertically confined flow conditions that can appear during inundations, due to the presence of hydraulic structures such as bridges, culverts, or underground river reaches. In this article we propose a new mathematical modification of the standard 2D‐SWE, inspired by the two‐component pressure approach for 1D flows, to address the issue of transient vertically confined flows including transitions between free surface and pressurized conditions. A finite volume discretization to solve the proposed system of equations is proposed and analyzed. Various test cases are used to show the numerical stability and accuracy of the discretization, and to validate the proposed formulation. Results show that the proposed method is numerically stable, accurate, mass conservative, and preserves the C‐property. It can also handle subcritical, supercritical, and transcritical flows under free surface or vertically confined conditions.

Flood Risk in Urban Areas: Modelling, Management and Adaptation to Climate Change. A Review

“…The only empirical parameter that must be defined by the user is the Manning roughness coefficient, the values of which are relatively well established in river engineering manuals as a function of land uses. To further improve flood-risk estimations, especially in the presence of in-line structures such as bridges, additional processes that occur during floods can be included within the two-dimensional shallow-water modelling, such as the transport of sediment or wood [63][64][65][66], or mixed free-surface-pressurized flows in vertically confined river reaches [67].…”

Efficient Design of Road Drainage Systems

“…Iber is a freely distributed 2D numerical tool (www.iberaula.com, accessed on 12 June 2021) initially developed for modeling hydrodynamic and sediment transport [19,[24][25][26][27][28] that solves the SWEs on irregular geometries using the finite volume method (FVM). The tool has been continuously enhanced since it was first presented in 2010, and now includes a series of modules for different fluvial and hydrological processes, such as rainfall-runoff transformation [29][30][31], water quality processes [32,33], large wood transport [34], physical habitat suitability assessment [35], the consideration of pressurized flow [36][37][38][39], and, more recently, non-Newtonian flows such as wood-laden flows [40] and snow avalanches [41,42].…”

Modelling Weirs in Two-Dimensional Shallow Water Models

“…A detailed mathematical description of the discretization schemes used in the model can be found in [18,23,24]. The model has been validated extensively and applied to a large number of open channel flow and river inundation studies [25][26][27][28]. The detailed characteristics of each of the tests corresponding to the experimental sets can be found in Appendix A.…”