Can the 2D shallow water equations model flow intrusion into buildings during urban floods?

The multiple flow paths existing in urban environments lead to complex flow fields during urban flooding. Modelling these flow processes with three-dimensional numerical models may be scientifically sound; however, such numerical models are computationally demanding. To ascertain whether urban floods can be modelled with faster tools, this study investigated for the first time the capacity of the 2D shallow water equations (SWE) in modelling the flow patterns within and around urban blocks with openings, i.e., involving flow exchanges between the flows in the streets and within the urban blocks (e.g., through alleys leading to courtyards or through broken windows or doors). Laboratory experiments of idealized urban floods were simulated with two academic 2D SWE models, with their most notable difference being the parameterization of the eddy viscosity. Specifically, the first model had a turbulence closure based on flow depth and friction velocity while the second model had a depth-averaged k-ε turbulence closure. Thirteen urban layouts were considered with steady flow and five with unsteady flow. Both models simulated the flow depths accurately for the steady cases. The discharge distribution in the streets and the flow velocities were predicted with lower accuracy, particularly in layouts with large open spaces. The average deviation of the modelled discharge distribution at the outlets was 2.5% and 7.3% for the first and second model, respectively. For the unsteady cases, only the first model was tested. It predicted well the velocity pattern during the falling limb of a flood wave, while it did not reproduce all recirculation zones in the rising limb. The peak flow depths in the streets and the peak discharges at the outlets were predicted with an average deviation of 6.7% and 8.6%, respectively. Even though some aspects of the flow in an urban setup are 3D, the findings of this study support the modelling of such processes with 2D SWE models.