A model for overland flow and associated processes within the Hydroinformatics Modelling System

Abstract

This paper presents a numerical model suitable for a broad range of surface flow problems such as overland flow, wetting and drying processes, varying flow conditions and shock waves. It is based on solution of two-dimensional fully dynamic shallow water equations using a cell-centred finite-volume method. Numerical fluxes are computed with a Harten, Lax and van Leer approximate Riemann solver with a contact wave restored. The scheme is second-order accurate in space, and a total variation diminishing method is used to avoid spurious oscillations in the solution. For extending the model to rainfall-runoff applications, infiltration is considered as a constant runoff coefficient and by the Green-Ampt model. The model is implemented in the Hydroinformatics Modelling System, an object-oriented framework that enables the implementation and simulation of single and multiple processes in different spatial and temporal resolutions, as well as their interactions. The capabilities of the model are shown by comparison with analytical solutions and experimental data of a flash flood and a surface runoff experiment. Finally, a real rainfall-runoff event in a small alpine catchment is investigated. Overall, good agreement of numerical and analytical results, as well as measurements, has been obtained. A area of the considered cell m 2 À Á C Chézy coefficient s m À1=6 À Á c concentration (À) D diffusion coefficient m 2 s À1 À Á d water depth (m) ε vegetation drag related coefficient η water elevation above datum: η ¼ z B þ d (m) f flux vector g standard gravity 9:81 m s À2 À Á Γ boundary of control volume (m) I cumulative infiltration (m) i infiltration rate m s À1 À Á K average residence time (s) k index of a face of the considered cell l k length of face k (m) m c contaminant source/sink term s À1 À Á m w water source/sink term m s À1 À Á n k normal vector pointing outwards of face k n Manning coefficient (s m À1=3 ) n time step index ∇ del operator: ∇ ¼ @ @x , @ @y T ν t turbulent kinematic viscosity m 2 s À1 À Á Ψ runoff coefficient (-) Q discharge m 3 s À1 À Á q vector of conserved flow variables r rainfall intensity m s À1 À Á ρ density of water kg m À3 À Á S storage (m 3 ) s source vector t time (s) Δt time step (s) u velocity component in x-direction m s À1 À Á v velocity component in y-direction m s À1 À Á v velocity vector V w specific soil water volume (m) x X coordinate (m) y Y coordinate (m) z B bottom elevation above datum (m) Ω control volume (m 2 )

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

“…The classical shallow water model used for obtaining the reference results is the model presented in Simons et al (2014). All simulations are run in parallel with 8 threads of an Intel Ò Core TM i7-2600 CPU (3.40 GHz).…”

“…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).…”

Upscaling the shallow water model with a novel roughness formulation

“…As shown in, e.g. Simons et al (2014), Smith et al (2007), every friction law coefficient can be transformed into the Chézy coefficient and therefore can be incorporated in Eq. 1.…”

“…A brief overview of the implementation is given below. For more detailed information, the reader is referred to Simons et al (2014).…”

“…Extensive numerical simulations of surface and subsurface runoff for this domain were carried out in Simons et al (2014), Stadler et al (2012) within Research Unit 'Coupling of flow and deformation processes for modelling the movement of natural slopes' funded by the German Research Foundation (Hinkelmann et al 2011). During these simulations, the model was calibrated with a runoff coefficient W ¼ 0:3 in combination with a linear reservoir model to account for the slower discharge component in the subsurface, which was identified as a crucial contributor to the discharge at the outlet of the domain.…”