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

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 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 modelsmore » 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.« less
Authors:
 [1] ;  [2] ;  [3] ;  [2]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Technische Univ. Berlin (Germany). Dept. of Civil Engineering
  2. Technische Univ. Berlin (Germany). Dept. of Civil Engineering
  3. Univ. of Cambridge (United Kingdom). Dept. of Engineering
Publication Date:
Grant/Contract Number:
AC02-05CH11231
Type:
Accepted Manuscript
Journal Name:
Water Science and Engineering
Additional Journal Information:
Journal Volume: 10; Journal Issue: 4; Journal ID: ISSN 1674-2370
Publisher:
Elsevier - Hohai University
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; Porosity; Macroscopic modeling of urban flooding; Wave propagation speed; Godunov flux; Single porosity shallow water model; Anisotropic porosity shallow water model
OSTI Identifier:
1482522

Özgen-Xian, Ilhan, Zhao, Jia-heng, Liang, Dong-fang, and Hinkelmann, Reinhard. Wave propagation speeds and source term influences in single and integral porosity shallow water equations. United States: N. p., Web. doi:10.1016/j.wse.2017.12.003.
Özgen-Xian, Ilhan, Zhao, Jia-heng, Liang, Dong-fang, & Hinkelmann, Reinhard. Wave propagation speeds and source term influences in single and integral porosity shallow water equations. United States. doi:10.1016/j.wse.2017.12.003.
Özgen-Xian, Ilhan, Zhao, Jia-heng, Liang, Dong-fang, and Hinkelmann, Reinhard. 2017. "Wave propagation speeds and source term influences in single and integral porosity shallow water equations". United States. doi:10.1016/j.wse.2017.12.003. https://www.osti.gov/servlets/purl/1482522.
@article{osti_1482522,
title = {Wave propagation speeds and source term influences in single and integral porosity shallow water equations},
author = {Özgen-Xian, Ilhan and Zhao, Jia-heng and Liang, Dong-fang and Hinkelmann, Reinhard},
abstractNote = {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 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.},
doi = {10.1016/j.wse.2017.12.003},
journal = {Water Science and Engineering},
number = 4,
volume = 10,
place = {United States},
year = {2017},
month = {12}
}