Upscaled shallow water modeling with SW2D-Lemon for urban flood simulation

2021 ◽  
Author(s):  
Joao Guilherme Caldas Steinstraesser ◽  
Carole Delenne ◽  
Pascal Finaud-Guyot ◽  
Vincent Guinot ◽  
Joseph Luis Kahn Casapia ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Solid Phase ◽  
Academic Research ◽  
Water Model ◽  
Graphic User Interface ◽  
Flood Simulation ◽  
Urban Flood ◽  
Transport Reaction ◽  
Head Losses

<p>We present a new multi-OS platform named SW2D-LEMON (SW2D for Shallow Water 2D) developed by the LEMON research team in Montpellier.</p><p>SW2D-LEMON is a multi-model software focusing on shallow water-based models. It includes an unprecedented collection of upscaled (porosity) models used for shallow water equations and transport-reaction processes. Porosity models are obtained by averaging the two-dimensional shallow water equations over large areas containing both a water and a solid phase. The size of a computational cell can be increased by a factor 10 to 50 compared to a 2D shallow water model, with CPU times reduced by 2 to 3 orders of magnitude. Applications include urban flood simulations as well as flows over complex topography. Besides the standard shallow water equations (the default model), several porosity models are included in the platform: (i) Single Porosity, (ii) Dual Integral Porosity, (iii) Depth-dependent Porosity. Various flow processes (friction, head losses, wind, momentum diffusion, precipitation/infiltration) can be included in a modular way by activating specific execution flags.</p><p>Classical input data are required by SW2D-Lemon software: mesh file (several formats available) with elements having an arbitrary number of edges; geometric and hydraulic parameter fields: bathymetry, porosity, Boussinesq/Coriolis momentum distribution coefficient, friction coefficient fields, etc.; initial and boundary conditions (several types available) and forcings (wind, rainfall).</p><p>SW2D can be used in two ways: in command-line mode or via a dedicated graphic user interface (GUI). Both features are available on all Windows, MacOS and Linux operating systems. SW2D is available under three license modes: Academic Research (source code, developer manual and basic configurations are freely available in the framework of a scientific partnership with the LEMON team), Industry and education.</p><p>Various real-world test cases will be presented to illustrate the potential of SW2D and the contribution of porosity based models to urban flood modelling:</p><ul>- Flood simulation on Sacramento city induced by the breach of a dike;</ul><ul>- Marine submersion on Valras Plage;</ul><ul>- Fast rain flood on the Abidjan Riviera district.</ul><p> </p>

scholarly journals Two-Dimensional Shallow-Water Model with Porosity for Urban Flood Modeling

Proceedings ◽  
2018 ◽  
Vol 2 (20) ◽  
pp. 1307
Author(s):  
Malika Benslimane ◽  
Saâdia Benmamar ◽  
André Paquier
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Urban Areas ◽  
Large Scale ◽  
Momentum Equation ◽  
Water Model ◽  
Finite Volume Scheme ◽  
Two Dimensional ◽  
Flood Modeling ◽  
Urban Flood

In the world, floods are at the forefront of natural hazard. Urban areas are often at risk of flooding and just as often unprepared for management. Flood modeling is nowadays a very important topic in the theme of water, it inevitably involves the numerical resolution of the shallow water equations derived from the Navier Stocks equations governing flows. Two-dimensional shallow water models with porosity appear as an interesting path for the large-scale modeling of floodplains with urbanized areas. The porosity accounts for the reduction in storage and in the exchange sections due to the presence of buildings and other structures in the floodplain. The introduction of a porosity into the two-dimensional shallow water equations leads to modified expressions for the fluxes and source terms. An extra source term appears in the momentum equation. The developed solution method consists in solving the two-dimensional shallow water equations with porosity via a finite volume scheme solving the conservative form of the equations which can be reduced to a calculation of flux through an edge, a problem that can be approached by a one-dimensional problem in the normal direction at the edge (Riemann problem).

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

scholarly journals A Well-balanced Finite Volume Scheme for Shallow Water Equations with Porosity: Application to Modelling Flow through Rigid Vegetation

2018 ◽  
Vol 40 ◽  
pp. 05032
Author(s):  
Minh H. Le ◽  
Virgile Dubos ◽  
Marina Oukacine ◽  
Nicole Goutal
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Simple Wave ◽  
Water Model ◽  
Strong Interactions ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Rigid Vegetation ◽  
Vertical Cylinders

Strong interactions exist between flow dynamics and vegetation in open-channel. Depth-averaged shallow water equations can be used for such a study. However, explicit representation of vegetation can lead to very high resolution of the mesh since the vegetation is often modelled as vertical cylinders. Our work aims to study the ability of a single porosity-based shallow water model for these applications. More attention on flux and source terms discretizations are required in order to archive the well-balancing and shock capturing properties. We present a new Godunov-type finite volume scheme based on a simple-wave approximation and compare it with some other methods in the literature. A first application with experimental data was performed.

On the necessity of non-hydrostatic pressure models for free surface flow over complex topography

2020 ◽  
Author(s):  
Isabel Echeverribar ◽  
Pilar Brufau ◽  
Pilar García-Navarro
Keyword(s):  
Free Surface ◽  
Hydrostatic Pressure ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Finite Volume Scheme ◽  
Complex Topography ◽  
Source Terms ◽  
Pressure Correction ◽  
Wide Range

<p><span><strong>There is a wide range of geophysical flows, such as flow in open channels and rivers, tsunami and flood modeling, that can be mathematically represented by the non-linear shallow water 1D equations involving hydrostatic pressure assumptions as an approximation of the Navier Stokes equations. In this context, special attention must be paid to bottom source terms integration and numerical corrections when dealing with wet/dry fronts or strong slopes in order to obtain physically-based solutions (Murillo and García-Navarro, 2010) in complex and realistic cases with irregular topography. However, although these numerical corrections have been developed in recent years achieving not only more robust models but also more accurate results, they still might find a limit when dealing with specific scenarios where vertical information or disspersive effects become crucial. This work presents a 1D shallow water model that introduces vertical information by means of a non-hydrostatic pressure correction when necessary. In particular, the pressure correction method (Hirsch, 2007) is applied to a 1D finite volume scheme for a rectification of the velocity field in free surface scenarios. It is solved by means of an implicit scheme, whereas the depth-integrated shallow water equations are solved using an explicit scheme. It is worth highlighting that it preserves all the advantages and numerical fixes aforementioned for the pure shallow water system. Computations with and without non-hydrostatic corrections are compared for the same cases to test the validity of the conventional hydrostatic pressure assumption at some scenarios involving complex topography.</strong></span></p><p><span>[1] J. Murillo and P. Garcia-Navarro, Weak solutions for partial differential equations with source terms: application to the shallow water equations, Journal of Computational Physics, vol. 229, iss. 11, pp. 4327-4368, 2010.</span></p><p><span>[2] C. Hirsch, Numerical Computation of Internal and External flows: The fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann, 2007.</span></p>

scholarly journals Symmetries and exact solutions of the rotating shallow-water equations

2009 ◽  
Vol 20 (5) ◽  
pp. 461-477 ◽  
Author(s):  
A. A. CHESNOKOV
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
New Class ◽  
New Exact Solutions ◽  
Time Periodic Solutions ◽  
Rotating Shallow Water ◽  
Rotating Shallow Water Equations ◽  
Time Periodic

Lie symmetry analysis is applied to study the non-linear rotating shallow-water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow-water equations can be transformed to the classical shallow-water model. The derived symmetries are used to generate new exact solutions of the rotating shallow-water equations. In particular, a new class of time-periodic solutions with quasi-closed particle trajectories is constructed and studied. The symmetry reduction method is also used to obtain some invariant solutions of the model. Examples of these solutions are presented with a brief physical interpretation.

scholarly journals Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation

2020 ◽  
Vol 28 (2) ◽  
pp. 93-114
Author(s):  
Stelian Ion ◽  
Stefan-Gicu Cruceanu ◽  
Dorin Marinescu
Keyword(s):  
Initial Data ◽  
Shallow Water ◽  
Global Solution ◽  
Riemann Problem ◽  
Hyperbolic System ◽  
Shallow Water Equations ◽  
Local Existence ◽  
Water Model ◽  
Constructive Approach ◽  
Shallow Water Model

AbstractWe investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be “small enough”). One di culty for the extended solution arises from the double degeneracy of the hyperbolic system describing the model. Another di culty is given by the fact that the construction of the solution assumes solving an equation which has no global solution. Finally, we present some cases to illustrate the existence and non-existence of the solution.

scholarly journals Urban flood modeling with porous shallow-water equations: A case study of model errors in the presence of anisotropic porosity

2015 ◽  
Vol 523 ◽  
pp. 680-692 ◽  
Author(s):  
Byunghyun Kim ◽  
Brett F. Sanders ◽  
James S. Famiglietti ◽  
Vincent Guinot
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Model Errors ◽  
Flood Modeling ◽  
Urban Flood

scholarly journals Shallow water equations for equatorial tsunami waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170100 ◽  
Author(s):  
Anna Geyer ◽  
Ronald Quirchmayr
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Water Model ◽  
Shallow Water Model ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Tsunami Waves ◽  
De Vries ◽  
Model Equations

We present derivations of shallow water model equations of Korteweg–de Vries and Boussinesq type for equatorial tsunami waves in the f -plane approximation and discuss their applicability. This article is part of the theme issue ‘Nonlinear water waves’.

scholarly journals Dual integral porosity shallow water model for urban flood modelling

2017 ◽  
Vol 103 ◽  
pp. 16-31 ◽  
Author(s):  
Vincent Guinot ◽  
Brett F. Sanders ◽  
Jochen E. Schubert
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model ◽  
Urban Flood ◽  
Flood Modelling ◽  
Urban Flood Modelling

scholarly journals Urban Stormwater Modeling with Local Inertial Approximation Form of Shallow Water Equations: A Comparative Study

2021 ◽  
Author(s):  
Weiqi Wang ◽  
Wenjie Chen ◽  
Guoru Huang
Keyword(s):  
Shallow Water ◽  
Computational Efficiency ◽  
Environmental Protection Agency ◽  
Shallow Water Equations ◽  
Drainage System ◽  
Flood Modeling ◽  
Urban Stormwater ◽  
Urban Flood ◽  
Storm Water Management Model ◽  
Form Model

AbstractThis study focused on the performance and limitations of the local inertial approximation form model (LIM) of the shallow water equations (SWEs) when applied in urban flood modeling. A numerical scheme of the LIM equations was created using finite volume method with a first-order spatiotemporal Roe Riemann solver. A simplified urban stormwater model (SUSM) considering surface and underground dual drainage system was constructed based on LIM and the US Environmental Protection Agency Storm Water Management Model. Moreover, a complete urban stormwater model (USM) based on the SWEs with the same solution algorithm was used as the evaluation benchmark. Numerical results of the SUSM and USM in a highly urbanized area under four rainfall return periods were analyzed and compared. The results reveal that the performance of the SUSM is highly consistent with that of the USM but with an improvement in computational efficiency of approximately 140%. In terms of the accuracy of the model, the SUSM slightly underestimates the water depth and velocity and is less accurate when dealing with supercritical flow in urban stormwater flood modeling. Overall, the SUSM can produce comparable results to USM with higher computational efficiency, which provides a simplified and alternative method for urban flood modeling.

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