Two-Dimensional Shallow-Water Model with Porosity for Urban Flood Modeling

In the world, floods are at the forefront of natural hazard. Urban areas are often at risk of flooding and just as often unprepared for management. Flood modeling is nowadays a very important topic in the theme of water, it inevitably involves the numerical resolution of the shallow water equations derived from the Navier Stocks equations governing flows. Two-dimensional shallow water models with porosity appear as an interesting path for the large-scale modeling of floodplains with urbanized areas. The porosity accounts for the reduction in storage and in the exchange sections due to the presence of buildings and other structures in the floodplain. The introduction of a porosity into the two-dimensional shallow water equations leads to modified expressions for the fluxes and source terms. An extra source term appears in the momentum equation. The developed solution method consists in solving the two-dimensional shallow water equations with porosity via a finite volume scheme solving the conservative form of the equations which can be reduced to a calculation of flux through an edge, a problem that can be approached by a one-dimensional problem in the normal direction at the edge (Riemann problem)