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.

Rotating Shallow-Water Models with Full Coriolis Force

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Coriolis Force ◽  
Shallow Water Equations ◽  
Vertical Component ◽  
Tangent Plane ◽  
Water Model ◽  
Shallow Water Models ◽  
Water Models ◽  
Rotating Shallow Water ◽  
Rotating Shallow Water Equations

The derivation of the rotating shallow-water model by vertical averaging is carried on in the tangent plane approximation without neglecting the vertical component of the Coriolis force, and contributions of the vertical component of velocity in its horizontal component (‘non-traditional’ terms), leading to one- and two-layer ‘non-traditional’ rotating shallow-water models. A similar approach on the whole sphere encounters difficulties with conservation of angular momentum. Consistent ‘non-traditional’ rotating shallow-water equations in this case are obtained from the variational principle, which is first formulated for full primitive equations. It is shown that columnar motion hypothesis should be replaced by solid-angle motion one on the sphere. Two-layer non-traditional rotating shallow-water equations are used to analyse inertial instability of jets and compare the results with Chapter 10. It is shown that non-traditional terms can increase the growth rates up to 30% in some configurations and can also change the structure of the unstable modes.

CONSERVATION LAWS FOR ONE-DIMENSIONAL SHALLOW WATER MODELS FOR ONE AND TWO-LAYER FLOWS

2006 ◽  
Vol 16 (01) ◽  
pp. 119-137 ◽  
Author(s):  
RICARDO BARROS
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Shallow Water Model ◽  
Frobenius Problem ◽  
One Dimensional ◽  
Shallow Water Models ◽  
The One ◽  
Open Question

A full set of conservation laws for the two-layer shallow water equations is presented for the one-dimensional case. We prove that all the conservation laws are linear combination of the equations for the conservation of mass and velocity (in each layer), total momentum and total energy.This result generalizes that of Montgomery and Moodie that found the same conserved quantities by restricting their search to the multinomials expressions in the layer variables. Though the question of whether or not there are only a finite number of these quantities is left as an open question by the authors. Our work puts an end to this: in fact, no more conservation laws are admitted for the two-layer shallow water equations. The key mathematical ingredient of the method proposed leading to the result is the Frobenius problem. Moreover, we present a full set of conservation laws for the classical one-dimensional shallow water model with topography, by using the same techniques.

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

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.

scholarly journals Towards district scale flood simulations using conventional and anisotropic porosity shallow water models with high-resolution topographic information

2018 ◽  
pp. 90-98
Author(s):  
Ilhan Özgen ◽  
Morgan Abily ◽  
Jiaheng Zhao ◽  
Dongfang Liang ◽  
Philippe Gourbesville ◽  
...  
Keyword(s):  
High Resolution ◽  
Shallow Water ◽  
Large Deviation ◽  
Computational Cost ◽  
Water Model ◽  
Shallow Water Model ◽  
Data Set ◽  
Shallow Water Models ◽  
Urban Catchments ◽  
Water Models

Current topographic survey technology provides high-resolution (HR) datasets for urban environments. Incorporating this HR information in models aiming to provide flood risk assessment is desirable because the flood wave propagation is depending on the urban topographic features, i.e. buildings, bridges and street networks. Conceptual, numerical and practical challenges arise from the application of shallow water models to HR urban flood modeling. For instance, numerical challenges are occurrence of wet-dry fronts, geometric discontinuities in the urban environment and discontinuous solutions, i.e. shock waves. These challenges can be overcome by using a Godunov-type scheme. However, the computational cost of this type of schemes is high, such that HR two-dimensional shallow water simulations with practical relevance have to be run on supercomputers. The porous shallow water model is an alternative approach that aims to reduce computational cost by using a coarse resolution and accounting for unresolved processes by means of the porosity terms. Usually, a speedup between two and three orders of magnitude in comparison to HR simulations can be obtained. This study reports preliminary results of a practical test case concerning pluvial flooding in a district of the city of Nice, France, caused by the intense rainfall event on October 3rd, 2015. HR topography data set on a 1 m resolution is available for the district, whereby street features of infra-metric dimensions have been included. A reference solution is calculated by a HR shallow water model on a 1 m by 1 m structured computational grid. The porous shallow water model is run on a 10 m by 10 m grid and the influence of the drag source term is studied. The model results show a large deviation, which is caused by the poor meshing strategy of the porous shallow water (AP) model. The study also summarizes practical challenges that arise during the application of the AP and HR models to a large urban catchment. The main difficulty is to obtain a good mesh. In smaller scale investigations, the mesh is currently constructed by hand such that the cell edges align with buildings. This approach is not feasible for large scale urban catchments with a large number of buildings. Future steps that have to be taken, such as a strategy for automatic mesh generation, are reported on.

SW2D-GPU: A two-dimensional shallow water model accelerated by GPGPU

2021 ◽  
pp. 105205
Author(s):  
Tomas Carlotto ◽  
Pedro Luiz Borges Chaffe ◽  
Camyla Innocente dos Santos ◽  
Seungsoo Lee
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model

Overland flow computations in urban and industrial catchments from direct precipitation data using a two-dimensional shallow water model

2010 ◽  
Vol 62 (9) ◽  
pp. 1998-2008 ◽  
Author(s):  
L. Cea ◽  
M. Garrido ◽  
J. Puertas ◽  
A. Jácome ◽  
H. Del Río ◽  
...  
Keyword(s):  
Shallow Water ◽  
Surface Runoff ◽  
Experimental Validation ◽  
Water Model ◽  
Storm Event ◽  
Precipitation Data ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Sewer Network ◽  
Direct Precipitation

This paper presents the experimental validation and the application to a real industrial catchment of a two-dimensional depth-averaged shallow water model used for the computation of rainfall-runoff transformation from direct precipitation data. Instead of using the common approach in flood inundation modelling, which consists in computing the water depth and velocity fields given the water discharge, in this study the rainfall intensity is imposed directly in the model, the surface runoff being generated automatically. The model considers infiltration losses simultaneously with flow simulation. Gullies are also included in the model, although the coupling between the surface runoff and the sewer network is not considered. Experimental validation of the model is presented in several simplified laboratory configurations of urban catchments, in which the surface runoff has been measured for different hyetographs. The application to a real industrial catchment includes a sewer network flow component, which is solved with the SWMM model. The numerical predictions of the discharge hydrograph generated by a 12 hours storm event are compared with field measurements, providing encouraging results.

scholarly journals Forcing for a Cascaded Lattice Boltzmann Shallow Water Model

Water ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 439 ◽  
Author(s):  
Sara Venturi ◽  
Silvia Di Francesco ◽  
Martin Geier ◽  
Piergiorgio Manciola
Keyword(s):  
Shallow Water ◽  
Lattice Boltzmann ◽  
Model Performance ◽  
Lattice Boltzmann Model ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Basic Scheme ◽  
Order Scheme ◽  
Boltzmann Model

This work compares three forcing schemes for a recently introduced cascaded lattice Boltzmann shallow water model: a basic scheme, a second-order scheme, and a centred scheme. Although the force is applied in the streaming step of the lattice Boltzmann model, the acceleration is also considered in the transformation to central moments. The model performance is tested for one and two dimensional benchmarks.

Investigation of the Importance of Spatial Resolution for Two-Dimensional Shallow-Water Model Accuracy

2009 ◽  
Vol 135 (11) ◽  
pp. 917-925 ◽  
Author(s):  
Siniša Družeta ◽  
Luka Sopta ◽  
Senka Maćešić ◽  
Nelida Črnjarić-Žic
Keyword(s):  
Shallow Water ◽  
Spatial Resolution ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Model Accuracy
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