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

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).

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Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽

10.3390/w13162152 ◽

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.

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

E3S Web of Conferences ◽

10.1051/e3sconf/20184005032 ◽

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.

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

10.5194/egusphere-egu2020-19946 ◽

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

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 Garc&#237;a-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.[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.[2] C. Hirsch, Numerical Computation of Internal and External flows: The fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann, 2007.

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Maximum power from a turbine farm in shallow water

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.515 ◽

2013 ◽

Vol 714 ◽

pp. 634-643 ◽

Cited By ~ 20

Author(s):

Chris Garrett ◽

Patrick Cummins

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Numerical Solutions ◽

Momentum Equation ◽

Basic Flow ◽

Maximum Power ◽

Two Dimensional ◽

Dominant Term ◽

Tidal Flows ◽

Linear Friction

AbstractThe maximum power that can be obtained from a confined array of turbines in steady or tidal flows is considered using the two-dimensional shallow-water equations and representing the turbine farm by a uniform local increase in friction within a circle. Analytical results supported by dimensional reasoning and numerical solutions show that the maximum power depends on the dominant term in the momentum equation for flows perturbed on the scale of the farm. If friction dominates in the basic flow, the maximum power is a fraction (half for linear friction and 0.75 for quadratic friction) of the dissipation within the circle in the undisturbed state; if the advective terms dominate, the maximum power is a fraction of the undisturbed kinetic energy flux into the front of the turbine farm; if the acceleration dominates, the maximum power is similar to that for the linear frictional case, but with the friction coefficient replaced by twice the tidal frequency.

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

Journal of Hydrology ◽

10.1016/j.jhydrol.2015.01.059 ◽

2015 ◽

Vol 523 ◽

pp. 680-692 ◽

Cited By ~ 46

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

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

International Journal of Disaster Risk Science ◽

10.1007/s13753-021-00368-0 ◽

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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SHALLOW WATER EQUATION SOLUTION IN 2D USING FINITE DIFFERENCE METHOD WITH EXPLICIT SCHEME

Jurnal Natural ◽

10.24815/jn.v17i2.7997 ◽

2017 ◽

Vol 17 (2) ◽

pp. 105

Author(s):

Nuraini Nuraini ◽

Syamsul Rizal ◽

Marwan Marwan

Keyword(s):

Finite Difference ◽

Shallow Water ◽

Shallow Water Equations ◽

Shallow Water Equation ◽

Mass Conservation ◽

Conservation Equation ◽

Water Model ◽

Two Dimensional ◽

Shallow Water Model ◽

Three Dimensional Model

Abstract. Modeling the dynamics of seawater typically uses a shallow water model. The shallow water model is derived from the mass conservation equation and the momentum set into shallow water equations. A two-dimensional shallow water equation alongside the model that is integrated with depth is described in numerical form. This equation can be solved by finite different methods either explicitly or implicitly. In this modeling, the two dimensional shallow water equations are described in discrete form using explicit schemes.Keyword: shallow water equation, finite difference and schema explisit.REFERENSI 1. Bunya, S., Westerink, J. J. dan Yoshimura. 2005. Discontinuous Boundary Implementation for the Shallow Water Equations. Int. J. Numer. Meth. Fluids. 47: 1451-1468.2. Kampf Jochen. 2009. Ocean Modelling For Beginners. Springer Heidelberg Dordrecht. London New York.3. Rezolla, L 2011. Numerical Methods for the Solution of Partial Diferential Equations. Trieste. International Schoolfor Advanced Studies.4. Natakussumah, K. D., Kusuma, S. B. M., Darmawan, H., Adityawan, B. M. Dan Farid, M. 2007. Pemodelan Hubungan Hujan dan Aliran Permukaan pada Suatu DAS dengan Metode Beda Hingga. ITB Sain dan Tek. 39: 97-123.5. Casulli, V. dan Walters, A. R. 2000. An unstructured grid, three-dimensional model based on the shallow water equations. Int. J. Numer. Meth. Fluids. 32: 331-348.6. Triatmodjo, B. 2002. Metode Numerik Beta Offset. Yogyakarta.

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Two-dimensional shallow-water model with porosity for urban flood modelling

Journal of Hydraulic Research ◽

10.1080/00221686.2008.9521842 ◽

2008 ◽

Vol 46 (1) ◽

pp. 45-64 ◽

Cited By ~ 92

Author(s):

Sandra Soares-Frazão ◽

Julien Lhomme ◽

Vincent Guinot ◽

Yves Zech

Keyword(s):

Shallow Water ◽

Water Model ◽

Two Dimensional ◽

Shallow Water Model ◽

Urban Flood ◽

Flood Modelling ◽

Urban Flood Modelling

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Post-Wildfire Numerical Modeling for Flood Risk Management

10.5194/egusphere-egu2020-22181 ◽

2020 ◽

Author(s):

Ian Floyd ◽

Stanford Gibson ◽

Gaurav Savant ◽

Alejandro Sanchez ◽

Ronald Heath

Keyword(s):

Shallow Water ◽

Debris Flows ◽

Large Scale ◽

Numerical Models ◽

The United States ◽

Water Model ◽

Sediment Runoff ◽

Two Dimensional ◽

Model Framework ◽

Model Library

The number and intensity of large wildfires in is a growing concern in the United States.&#160; Over the past decade, the National Interagency Fire Centre (NSTC, 2015) reported increases of large fires in every western state in the arid and semi-arid western U.S.&#160; Wildfires, remove vegetation, reduce organic soil horizons to ash, extirpate microbial communities, alters soil structure, and potential development of hydrophobic soils.&#160; These processes all increase water and sediment runoff. Post-wildfire environments can cause a spectrum of hydrologic and sedimentation responses ranging from no response to catastrophic floods and deadly debris flows. Numerical modellers have developed a variety of Newtonian and non-Newtonian shallow-water algorithms to simulate each of these physical processes &#8211; making it difficult to model the range of post-wildfire flood conditions and understand model assumption and limitations. This makes a modular non-Newtonian computation library advantageous. This work presents a flexible, numerical model, library framework &#8216;DebrisLib&#8217; to simulate large-scale, post-wildfire non-Newtonian flows using diverse shallow-water parents code architecture. This work presents the non-Newtonian model framework effectiveness by linking it with two different modelling frameworks, specifically the diffusive-wave one-dimensional and two-dimensional Hydrologic Engineering Center River Analysis System (HEC-RAS), and shallow-water two-dimensional Adaptive Hydraulics (AdH) numerical models. The model library was verified and validated using three flume experiments for mud flows, hyperconcentrated flows, and debris flows under steady and unsteady flow conditions. Additionally the shallow-water model library framework linked with the 1D Hydrologic Engineering Centre Hydrologic Modelling System (HEC-HMS) successfully predicted the 2018 post-wildfire flooding and debris flows following the 2017 Thomas Fire near Santa Barbara, California.

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

10.5194/egusphere-egu21-8212 ◽

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

We present a new multi-OS platform named SW2D-LEMON (SW2D for Shallow Water 2D) developed by the LEMON research team in Montpellier.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.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).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.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:<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>&#160;

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