Mass and momentum conservation in the simplified flood routing models

Gąsiorowski, Dariusz; Szymkiewicz, Romuald

doi:10.1016/j.jhydrol.2007.08.017

Cited by 20 publications

(13 citation statements)

References 6 publications

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“…It is worth adding that a nonlinear diffusive wave equation with the water surface elevation H, as a dependent variable, is conservative. However, as has been presented by Gąsiorowski and Szymkiewicz [39] for 1D flood routing problems, the same equation with discharge Q satisfying mass principle cannot be derived.…”

Section: Methodsmentioning

confidence: 96%

Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems

Artichowicz¹,

Gąsiorowski²

2019

Water

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This paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed algorithm of the solution minimizes the numerical errors and is unconditionally stable. Consequently, it is possible to perform computations with a significantly greater time step than in the case of the explicit scheme. An additional efficiency improvement was achieved using the symmetry of the tridiagonal matrix of the arising system of nonlinear equations, due to the application of the parallelization strategy. The computational experiments showed that the proposed parallel implementation of the implicit scheme is very effective, at about two orders of magnitude with regard to computational time, in comparison with the explicit one.

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Section: Methodsmentioning

confidence: 96%

Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems

Artichowicz¹,

Gąsiorowski²

2019

Water

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“…It should be noted that, when the inflow hydrograph contains wave shocks, the numerical kinematic wave method may lead to mass balance and travel speed errors [14]; but under normal conditions, the mass balance errors may be neglected [11]. In our study, the daily inflow hydrograph from a hillslopes to a channel was simplified as a double-exponential function, the small mass-balance errors resulting from temporal and spatial discretization were further eliminated by assuming that the water storage in a channel cannot be negative, and the residual water that has not flowed out of the outlet of a channel remains as storage of the channel.…”

Section: Depth Of Water and Kinematic Wave Celerity For A Rectangulamentioning

confidence: 99%

Implementation of channel-routing routines in the Water Erosion Prediction Project (WEPP) model

Wang¹,

Wu²,

Elliott³

et al. 2010

Proceedings of the 2009 SIAM Conference on “Mathematics for Industry”

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The Water Erosion Prediction Project (WEPP) model is a process-based, continuous-simulation, watershed hydrology and erosion model. It is an important tool for water erosion simulation owing to its unique functionality in representing diverse landuse and management conditions. Its applicability is limited to relatively small watersheds since its current version does not simulate flow in permanent channels. In this study we developed a channel-routing module to simulate water flow in a permanent channel network. The module can utilize two methods: numerical kinematic-wave method and Muskingum-Cunge method. Results showed that, for appropriate temporal and spatial discretizations, both numerical solutions compared well with analytical solution of kinematic wave equations for simplified cases; otherwise, numerical dissipation from the kinematic wave solution, and numerical dispersion from the Muskingum-Cunge solution would occur.

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“…Mathematical modelling is often used to analyse hydrological phenomena (Gąsiorowski and Szymkiewicz, 2007;Gąsiorowski and Artichowicz, 2016). Most often, such analyses are performed in the case of uncontrolled catchments, when there is no other possibility to calculate design flow and control flow or other characteristic flows (Wałęga, 2013;Egiazarova et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Flood Management System in the City of Gdańsk, Oruński Stream Case Study

Kolerski¹,

Kalinowska²

2019

Acta Sci. Pol. Formatio Circumiectus

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Aim of the study This study analyses the efficiency of flood protection in a small urban catchment, based on a system of small reservoirs. Material and methods To assess the flood routing and surge reduction, a mathematical model of the river catchment was implemented. This was a lumped hydrological model, based on the SCS-CN method. Channel routing was performed, using kinematic wave equation. The sub-catchments have been determined based on the topographic maps and rain sewage systems. In the paper, the hydrological model of the water system of Potok Oruński (Oruński Stream) is presented with particular focus on the new and renovated retention structures. Hydrological modelling system of HEC HMS was used to simulate the catchment's response to precipitation. Thanks to the recently established monitoring system of the Oruński Stream, it was possible to calibrate and validate the model. Single rain episode from April 2018 was used to perform model calibration, proving its high compatibility. The calibrated model was then used to reproduce the flood surge of July 2001, using historical catchment data. The peak discharge demonstrated a need for additional retention in the studied catchment. Theoretical scenarios were also modelled. The precipitation volume was calculated based on the IFS. As a worst-case scenario, the rain producing the most intense surface runoff was included. In all simulations, historical conditions as well the current state (2018) and projected further urbanisation of the catchment were taken into consideration. Results and conclusions Results of the study have shown reduction of the historical flood surge from July 2001 by nearly 60% when all existing flood protection systems were used.

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Mass and momentum conservation in the simplified flood routing models

Cited by 20 publications

References 6 publications

Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems

Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems

Implementation of channel-routing routines in the Water Erosion Prediction Project (WEPP) model

Mathematical Modeling of Flood Management System in the City of Gdańsk, Oruński Stream Case Study

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