Shallow water simulation of overland flows in idealised catchments

Liang, Dongfang; Özgen, Ilhan; Hinkelmann, Reinhard; Xiao, Yang; Chen, Jack M.

doi:10.1007/s12665-015-4744-5

Cited by 32 publications

(30 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Comparison among the runoff processes in different conditions indicates that smaller rainfall intensity, milder ground slope, or larger surface roughness leads to larger time of concentration. The same conclusion can be drawn from Equation and is consistent with numerous previous researches (Gottardi & Venutelli, , ; Jaber & Mohtar, ; Liang et al, ; Xiao et al, ).…”

Section: Comparison Between the Analytical And Experimental Resultssupporting

confidence: 92%

“…Thus, the accurate quantification of the overland flow process is key to predicting the transport of pollutants. Numerous studies have developed numerical models to simulate the one‐dimensional overland flows over a rectangular catchment (Gottardi & Venutelli, , ; Jaber & Mohtar, ; Liang, Özgen, Hinkelmann, Xiao, & Chen, ), and the results show that these models match well with the analytical solution of a kinematic wave model in idealized situations (Stephenson & Meadows, ). The analytical solution can be described as

t_{c} = {[L / (α I^{m - 1})]}^{1 / m}

q_{t} = α {(h)}^{m} = α {(italicIt)}^{m}, 0 \leq t \leq t_{c}

\begin{matrix} centertrue \\ center q_{t} = α {((), h)}^{m} = α {((), {italicIt}_{c})}^{m} = LI, & center t_{c} \leq t \leq T \end{matrix}

\begin{matrix} centertrue \\ center q_{t} = LI - I^{m} α^{1 / m} {q_{t}}^{1 - 1 / m} (t - T), & center T \leq t \end{matrix}

Q_{t} = q_{t} B,

where t c is the time of concentration (s); T is the rainfall duration (s); L is the length of the watershed (m); B is the width of the watershed (m); q t is the unit width flow rate (m 2 /s); h is the water depth (m); α can be defined as overcurrent capability coefficient (m 1/3 /s); m is a dimensionless water depth index.…”

Section: Mathematical Modelmentioning

confidence: 91%

See 1 more Smart Citation

Analytical and experimental study on dissolved pollutant wash‐off over impervious surfaces

Xiao

Zhang

Wang

et al. 2017

Hydrological Processes

Self Cite

View full text Add to dashboard Cite

Non‐point source pollution in the impervious surface of city, which including dissolved and particulate pollutants, is a significant source of water pollution. Simple first‐order decay models can generally simulate the cumulative wash‐off process of the particulate pollutants. There is inadequate knowledge as to whether or not they are suitable for dissolved pollutants. This study presents a mathematical wash‐off model for dissolved pollutants, which combines analytical equations for overland flows and the exponential equation for the pollutant wash‐off. A series of laboratory experiments have been conducted to verify this wash‐off model. It shows that the pollutant concentration and pollutant transport rate can be predicted well by the newly developed equations. It is found that the pollutant concentration monotonically decreases to zero as the accumulated pollutants are washed off, whereas the pollutant transport rate first increases to the maximum value and then decreases to zero. The maximum pollutant transport rate is found to increase with the decrease of the arrival time of the maximum value. The difference between the simplified exponential model and the amended wash‐off equation depends on the initial residual percentage (Pc), but the present equation generally provides a more accurate representation of the wash‐off process of dissolved pollutants.

show abstract

Section: Comparison Between the Analytical And Experimental Resultssupporting

confidence: 92%

t_{c} = {[L / (α I^{m - 1})]}^{1 / m}

q_{t} = α {(h)}^{m} = α {(italicIt)}^{m}, 0 \leq t \leq t_{c}

\begin{matrix} centertrue \\ center q_{t} = α {((), h)}^{m} = α {((), {italicIt}_{c})}^{m} = LI, & center t_{c} \leq t \leq T \end{matrix}

\begin{matrix} centertrue \\ center q_{t} = LI - I^{m} α^{1 / m} {q_{t}}^{1 - 1 / m} (t - T), & center T \leq t \end{matrix}

Q_{t} = q_{t} B,

Section: Mathematical Modelmentioning

confidence: 91%

Analytical and experimental study on dissolved pollutant wash‐off over impervious surfaces

Xiao

Zhang

Wang

et al. 2017

Hydrological Processes

Self Cite

View full text Add to dashboard Cite

show abstract

“…In shallow water modeling of river hydraulics (Özgen et al, 2013;Kesserwani and Liang, 2015), urban flooding (Liang, 2010;Mignot et al, 2006), urban runoff (Cea et al, 2010;Liang et al, 2007;Liang et al, 2015) and rainfall-runoff on natural environments (Mügler et al, 2011;Özgen et al, 2015;Simons et al, 2014;Viero et al 2014), the topographical features have a large influence on the numerical results. The availability of digital elevation data has increased significantly due to recent improvements in surveying technology, notably laser scanning and light detection and ranging (LIDAR) technologies, which provide high-resolution data sets at relatively low cost (Gessner et al, 2014;Gourbesville, 2009).…”

Section: Introductionmentioning

confidence: 99%

Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity

Özgen

Zhao

Liang

et al. 2016

Journal of Hydrology

Self Cite

View full text Add to dashboard Cite

Hinkelmann, R. (2016). Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity. Journal of Hydrology, 541, 1165Hydrology, 541, -1184Hydrology, 541, . https://doi.org/10.1016Hydrology, 541, /j.jhydrol.2016 Özgen, I.; Zhao, J.; Liang, D.; Hinkelmann, R.Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity The shallow water model with anisotropic porosity conceptually takes into account the unresolved subgrid-scale features, e.g. microtopography or buildings. This enables computationally efficient simulations that can be run on coarser grids, whereas reasonable accuracy is maintained via the introduction of porosity. This article presents a novel numerical model for the depth-averaged equations with anisotropic porosity. The porosity is calculated using the probability mass function of the subgrid-scale features in each cell and updated in each time step. The model is tested in a one-dimensional theoretical benchmark before being evaluated against measurements and high-resolution predictions in three case studies: a dam-break over a triangular bottom sill, a dam-break through an idealized city and a rainfall-runoff event in an idealized urban catchment. The physical processes could be approximated relatively well with the anisotropic porosity shallow water model. The computational resolution influences the porosities calculated at the cell edges and therefore has a large influence on the quality of the solution. The computational time decreased significantly, on average three orders of magnitude, in comparison to the classical high-resolution shallow water model simulation.

show abstract

“…The techniques of premodifying Riemann variables and constraining slope gradients are widely adopted by other researchers to develop SWE‐based models [e.g., Liang and Borthwick , ; Duran et al ., ; Duran , ; Bouchut and de Luna , ]. These models appear to be efficient and stable for simulations involving wetting and drying and have been widely used in practical applications [e.g., Hou et al ., ; Wang et al ., ; Marche et al ., ; Mangeney et al ., ; Liang et al ., ]. A number of other effective numerical schemes [e.g., George , ; Murillo and García‐Navarro , ] have also been reported in the literature, which apply similar slope gradient constrained technique at the wet‐dry interfaces but directly solve the Riemann problems incorporating source terms.…”

Section: Introductionmentioning

confidence: 99%

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

Xia

Liang

Ming

et al. 2017

Water Resources Research

151

View full text Add to dashboard Cite

Numerical models solving the full 2‐D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large‐scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2 Haltwhistle Burn, UK.

show abstract

Shallow water simulation of overland flows in idealised catchments

Cited by 32 publications

References 26 publications

Analytical and experimental study on dissolved pollutant wash‐off over impervious surfaces

Analytical and experimental study on dissolved pollutant wash‐off over impervious surfaces

Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

Contact Info

Product

Resources

About