Water Science and Engineering 2017, 10(4) 275-286 DOI:   https://doi.org/10.1016/j.wse.2017.12.003  ISSN: 1674-2370 CN: 32-1785/TV

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Keywords
Porosity
Macroscopic modeling of urban flooding
Wave propagation speed
Godunov flux
Single porosity shallow water model
Anisotropic porosity shallow water model
Authors
PubMed

Wave propagation speeds and source term influences in single and integral porosity shallow water equations

Ilhan Özgen a, *, Jia-heng Zhao a, Dong-fang Liang b, Reinhard Hinkelmann a

a Department of Civil Engineering, Technische Universität Berlin, Berlin 13355, Germany
b Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK

Abstract

In urban flood modeling, so-called porosity shallow water equations (PSWEs), which conceptually account for unresolved structures, e.g., buildings, are a promising approach to addressing high CPU times associated with state-of-the-art explicit numerical methods. The PSWE can be formulated with a single porosity term, referred to as the single porosity shallow water model (SP model), which accounts for both the reduced storage in the cell and the reduced conveyance, or with two porosity terms: one accounting for the reduced storage in the cell and another accounting for the reduced conveyance. The latter form is referred to as an integral or anisotropic porosity shallow water model (AP model). The aim of this study was to analyze the differences in wave propagation speeds of the SP model and the AP model and the implications of numerical model results. First, augmented Roe-type solutions were used to assess the influence of the source terms appearing in both models. It is shown that the different source terms have different influences on the stability of the models. Second, four computational test cases were presented and the numerical models were compared. It is observed in the eigenvalue-based analysis as well as in the computational test cases that the models converge if the conveyance porosity in the AP model is close to the storage porosity. If the porosity values differ significantly, the AP model yields different wave propagation speeds and numerical fluxes from those of the BP model. In this study, the ratio between the conveyance and storage porosities was determined to be the most significant parameter.

Keywords Porosity   Macroscopic modeling of urban flooding   Wave propagation speed   Godunov flux   Single porosity shallow water model   Anisotropic porosity shallow water model  
Received 2017-04-26 Revised 2017-07-19 Online: 2017-10-30 
DOI: https://doi.org/10.1016/j.wse.2017.12.003
Fund:
Corresponding Authors: ilhan.oezgen@wahyd.tu-berlin.de (Ilhan ?zgen)
Email: ilhan.oezgen@wahyd.tu-berlin.de
About author:

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