A note on weak shock wave reflection

2019

Journal of Hydrology

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.

Section: Additional Remarks On the Dual Porosity Subgrid Modelmentioning

confidence: 84%

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

2019

Journal of Hydrology

“…The numerical model solves the depth-averaged shallow water equations, written in conservative vector form, using a Godunov-type method on unstructured triangular grids [24][25][26]. To properly deal with sloping channel, the model uses a second-order accurate description of the channel bed, i.e., bottom elevations are defined at the grid nodes and are assumed to vary linearly within each element of the mesh [27,28].…”

Section: The Numerical Modelmentioning

confidence: 99%

Positive Surge Propagation in Sloping Channels

Peruzzo

Defina

2017

Water

A simplified model for the upstream propagation of a positive surge in a sloping, rectangular channel is presented. The model is based on the assumptions of a flat water surface and negligible energy dissipation downstream of the surge, which is generated by the instantaneous closure of a downstream gate. Under these hypotheses, a set of equations that depends only on time accurately describes the surge wave propagation. When the Froude number of the incoming flow is relatively small, an approximate analytical solution is also proposed. The predictive ability of the model is validated by comparing the model results with the results of an experimental investigation and with the results of a numerical model that solves the full shallow water equations

“…It's worth noting that the assumption of mutually orthogonal principal direction can be removed by considering different angles for each principal axes [12]; nonetheless, the effectiveness of the tensorial representation of conveyance porosity, the existence of (and the possibility of detecting) principal directions, and the computation of hydraulically significant conveyance porosities in real urban layouts are questionable tasks that deserve further investigation. At the moment, the model does not account for building drag (this can be included according to [12]), nor for transient momentum dissipation due to shock wave reflection [12,34], since the model is not intended to deal with supercritical flows nor with shock waves.…”

Section: Porosity Treatment Of Urbanized Areasmentioning

confidence: 99%

Modelling urban floods using a finite element staggered scheme with porosity and anisotropic resistance

2018

E3S Web Conf.

Artificial porosity models for urban flooding use porosity as a statistical descriptor for the presence of buildings, which are then treated as subgridscale features. Computational efficiency makes porosity models attractive for large-scale applications. These models are typically implemented in the framework of two-dimensional (2D) finite volume collocated schemes. The most effective schemes, falling under the category of Integral Porosity models, allow accounting for a wealth of sub-grid processes, but they are known to suffer from oversensitivity to mesh design in the case of anisotropic porosity fields. In the present exploratory study, a dual porosity approach is implemented into a staggered finite element numerical model. The free surface elevation is defined at grid nodes, where continuity equation is solved; fluxes are conveyed by triangular cells, which act as 2D-links between adjacent grid nodes. The presence of building is modelled using an isotropic porosity in the continuity equation to account for the reduced water storage, and an anisotropic conveyance porosity in the momentum equations to compute bottom shear stress. Both porosities are defined on an element-by-element basis, thus avoiding mesh-dependency. Although suffering a number of limitations, the model shows promising results.