Abstract
In the context of large-scale urban flood modeling, porosity shallow-water models enable a considerable speed-up in computations while preserving information on subgrid topography. Over the last two decades, major improvements have been brought to these models, but a single generally accepted model formulation has not yet been reached. Instead, existing models vary in many respects. Some studies define porosity parameters at the scale of the computational cells or cell interfaces, while others treat the urban area as a continuum and introduce statistically defined porosity parameters. The porosity parameters are considered either isotropic or anisotropic and depth-independent or depth-dependent. The underlying flow models are based either on the full shallow-water equations or approximations thereof, with various flow resistance parameterizations. Here, we provide a review of the spectrum of porosity models developed so far for large-scale urban flood modeling.
Highlights
The reasoning underpinning the first porosity shallow-water models consists in idealizing the urban area as a fictitious continuum, in which the flow properties are described by statistical averages at a scale much larger than the scale of individual obstacles and pathways, and sufficiently small compared to the extent of the whole urban area
This type of approach is widely used for modeling flow in porous media [14], such as in groundwater modeling, and it relies on the concept of representative elementary volume (REV)
By phase-averaging the standard shallow-water equations over a REV containing fluid and obstacles, porosity shallow-water equations were derived by Guinot and SoaresFrazão (2006) [10] (Figure 2)
Summary
Porosity shallow-water models are based on a relatively coarse computational mesh, while so-called porosity parameters are introduced to account for topographic information available at a subgrid-scale [9,10]. This approach is similar to common practice in modeling flow in porous media, such as in groundwater modeling [14].
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