Modelling urban floods using a finite element staggered scheme with an anisotropic dual porosity model

Abstract

In porosity models for urban flooding, artificial porosity is used as a statistical descriptor of the urban medium. Buildings are treated as subgrid-scale features and, even with the use of relatively coarse grids, their effects on the flow are accounted for. Porosity models are attractive for large-scale applications due to limited computational demand with respect to solving the classical Shallow Water Equations on high-resolution grids. In the last decade, effective schemes have been developed that allowed accounting for a wealth of sub-grid processes; unfortunately, they are known to suffer from oversensitivity to mesh design in the case of anisotropic porosity fields, which are typical of urban layouts. In the present study, a dual porosity approach is implemented into a two-dimensional Finite Element numerical scheme that uses a staggered unstructured mesh. The presence of buildings is modelled using an isotropic porosity in the continuity equation, to account for the reduced water storage, and a tensor formulation for conveyance porosity in the momentum equations, to account for anisotropy and effective flow velocity. The element-by-element definition of porosities, and the use of a staggered grid in which triangular cells convey fluxes and continuity is balanced at grid nodes, allow avoiding undesired mesh-dependency. Tested against refined numerical solutions and data from a laboratory experiment, the model provided satisfactory results. Model limitations are discussed in view of applications to more complex, real urban layouts.

A PCA spatial pattern based artificial neural network downscaling model for urban flood hazard assessment

“…However, such models remain too computationally demanding in the current state of computer technology to be applicable to entire conurbations within reasonable computational times. For this reason, upscaled shallow water models have been under development over the past two decades [3,4,9,17,20,23,25,28,29,27,30,54,43,48]. A salient advantage of upscaled shallow water models is their computational efficiency, with CPU times two to three orders of magnitude smaller than those of classical shallow water models [25,28,36].…”

Porosity Models for Large-Scale Urban Flood Modelling: A Review

“…In all models, this storage porosity is consistently evaluated as the ratio of the volume of void in-between obstacles to the volume of a considered control volume. The other effects are accounted for in various ways, such as by means of additional porosity parameters characterizing the flow conveyance along with specific directions [9,11,[15][16][17] or through directional flow resistance terms expressed in the tensor form [18,19].…”

“…Porosity parameters are defined either as statistical descriptors of the urban area at large-scale [10,20] or from local geometric features [9,11,21]; • Models include either a single [10,20] or multiple porosity parameters [9,11,[15][16][17]; • Effect of porosity in model fluxes and source terms is either isotropic [10,20] or anisotropic [9,11,12,15,16,[21][22][23]; • Porosity parameters are either depth-independent [9][10][11]17] or depth-dependent [12,22,23]; • Models are expressed in differential [10,20,21] or in integral form [9,11]; Moreover, the underlying flow model may correspond to the complete shallow-water equations (dynamic wave) [9][10][11][12]15,20,22,23] or to an approximation thereof, such as the diffusive wave [24][25][26]. Porosity as a statistical descri...…”

Effect of Independent Variables on Urban Flood Models

“…Many studies were undertaken by researchers in the field of flood disasters [2][3][4][5]. Recently, new modeling methods were proposed in attempts at urban flood simulation [6][7][8]. Urban flood models are widely used as a reliable tool in flood management.…”