The University of Southampton
University of Southampton Institutional Repository

Improving the stability of a simple formulation of the shallow water equations for 2-D flood modeling

Improving the stability of a simple formulation of the shallow water equations for 2-D flood modeling
Improving the stability of a simple formulation of the shallow water equations for 2-D flood modeling
The ability of two-dimensional hydrodynamic models to accurately and efficiently predict the propagation of floods over large urban areas is of paramount importance for flood risk assessment and management. Paradoxically, it is in these highly relevant urban domains where flood modeling faces some of the most challenging obstacles. This is because of the very high-resolution topography that is typically required to capture key hydraulic features, which significantly increases the computational time of the model. One particularly interesting solution to this difficulty was recently proposed in the form of a numerical scheme for the solution of a simplified version of the shallow water equations, which yields a system of two explicit equations that captures the most relevant hydraulic processes at very high computational efficiency. However, some stability problems were reported, especially when this formulation is applied to low friction areas. This is of particular importance in urban areas, where smooth surfaces are usually abundant. This paper proposes and tests two modifications of this previous numerical scheme that considerably improves the numerical stability of the model. Model improvements were assessed against a structured set of idealized test cases and finally in the simulation of flood propagation over complex topography in a highly urbanized area in London, United Kingdom. The enhanced stability achieved by the new formulation comes at no significant additional computational cost and, in fact, the model performance can benefit from the longer time steps that are allowed by the new scheme.
2-D model, flood modeling, flood risk, numerical model, shallow water, urban flood
0043-1397
W05528-[14pp]
de Almeida, Gustavo A. M.
f6edffc1-7bb3-443f-8829-e471b6514a7e
Bates, Paul D.
253914fc-226e-4904-9fa3-ac464a1756c2
Freer, Jim
fc5a6615-927e-4d47-8c56-14153e5621bf
Souvignet, Maxime
00ab537e-b305-4ea5-b383-0c456ec03bd9
de Almeida, Gustavo A. M.
f6edffc1-7bb3-443f-8829-e471b6514a7e
Bates, Paul D.
253914fc-226e-4904-9fa3-ac464a1756c2
Freer, Jim
fc5a6615-927e-4d47-8c56-14153e5621bf
Souvignet, Maxime
00ab537e-b305-4ea5-b383-0c456ec03bd9

de Almeida, Gustavo A. M., Bates, Paul D., Freer, Jim and Souvignet, Maxime (2012) Improving the stability of a simple formulation of the shallow water equations for 2-D flood modeling. Water Resources Research, 48 (5), W05528-[14pp]. (doi:10.1029/2011WR011570).

Record type: Article

Abstract

The ability of two-dimensional hydrodynamic models to accurately and efficiently predict the propagation of floods over large urban areas is of paramount importance for flood risk assessment and management. Paradoxically, it is in these highly relevant urban domains where flood modeling faces some of the most challenging obstacles. This is because of the very high-resolution topography that is typically required to capture key hydraulic features, which significantly increases the computational time of the model. One particularly interesting solution to this difficulty was recently proposed in the form of a numerical scheme for the solution of a simplified version of the shallow water equations, which yields a system of two explicit equations that captures the most relevant hydraulic processes at very high computational efficiency. However, some stability problems were reported, especially when this formulation is applied to low friction areas. This is of particular importance in urban areas, where smooth surfaces are usually abundant. This paper proposes and tests two modifications of this previous numerical scheme that considerably improves the numerical stability of the model. Model improvements were assessed against a structured set of idealized test cases and finally in the simulation of flood propagation over complex topography in a highly urbanized area in London, United Kingdom. The enhanced stability achieved by the new formulation comes at no significant additional computational cost and, in fact, the model performance can benefit from the longer time steps that are allowed by the new scheme.

Text
WRR_2012.pdf - Accepted Manuscript
Restricted to Registered users only
Download (3MB)
Request a copy
Text
WRR_2012.pdf - Accepted Manuscript
Download (3MB)

More information

Published date: May 2012
Keywords: 2-D model, flood modeling, flood risk, numerical model, shallow water, urban flood
Organisations: Water & Environmental Engineering Group

Identifiers

Local EPrints ID: 356385
URI: https://eprints.soton.ac.uk/id/eprint/356385
ISSN: 0043-1397
PURE UUID: cc32e7dd-adb7-434f-8ca7-73fcd48638ee
ORCID for Gustavo A. M. de Almeida: ORCID iD orcid.org/0000-0002-3291-3985

Catalogue record

Date deposited: 10 Sep 2013 12:59
Last modified: 19 Nov 2019 01:35

Export record

Altmetrics

Contributors

Author: Paul D. Bates
Author: Jim Freer
Author: Maxime Souvignet

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×