scholarly journals Towards a new friction model for shallow water equations through an interactive viscous layer

2019 ◽  
Vol 53 (1) ◽  
pp. 269-299 ◽  
Author(s):  
François James ◽  
Pierre-Yves Lagrée ◽  
Minh H. Le ◽  
Mathilde Legrand
Keyword(s):  
Shallow Water ◽  
Stokes Equations ◽  
Water Model ◽  
Finite Volume Scheme ◽  
Inviscid Fluid ◽  
Phase Lag ◽  
Viscous Layer ◽  
Viscous Effects ◽  
Shallow Water Models ◽  
Water Models

The derivation of shallow water models from Navier–Stokes equations is revisited yielding a class of two-layer shallow water models. An improved velocity profile is proposed, based on the superposition of an inviscid fluid and a viscous layer inspired by the Interactive Boundary Layer interaction used in aeronautics. This leads to a new friction law which depends not only on velocity and depth but also on the variations of velocity and thickness of the viscous layer. The resulting system is an extended shallow water model consisting of three depth-integrated equations: the first two are mass and momentum conservation in which a slight correction on hydrostatic pressure has been made; the third one, known as von Kármán equation, describes the evolution of the viscous layer. This coupled model is shown to be conditionally hyperbolic, and a Godunov-type finite volume scheme is also proposed. Several numerical examples are provided and compared to the Multi-Layer Saint-Venant model. They emphasize the ability of the model to deal with unsteady viscous effects. They illustrate also the phase-lag between friction and topography, and even recover possible reverse flows.

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 Finite-Volume Solvers for a Multilayer Saint-Venant System

2007 ◽  
Vol 17 (3) ◽  
pp. 311-320 ◽  
Author(s):  
Emmanuel Audusse ◽  
Marie-Odile Bristeau
Keyword(s):  
Shallow Water ◽  
Numerical Investigation ◽  
Finite Volume ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Relevant Alternative ◽  
Navier Stokes Equations ◽  
Numerical Tests ◽  
Shallow Water Models ◽  
Water Models

Finite-Volume Solvers for a Multilayer Saint-Venant SystemWe consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to 3D hydrostatic Navier-Stokes equations.

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.

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.

scholarly journals Development of a diffusive wave shallow water model with a novel stability condition and other new features

2017 ◽  
Vol 19 (3) ◽  
pp. 405-425 ◽  
Author(s):  
Mitra Jahanbazi ◽  
Ilhan Özgen ◽  
Rui Aleixo ◽  
Reinhard Hinkelmann
Keyword(s):  
Shallow Water ◽  
Stability Condition ◽  
Overland Flow ◽  
Time Integration ◽  
Free Fall ◽  
Wave Model ◽  
Water Model ◽  
Fall Velocity ◽  
Shallow Water Models ◽  
Water Models

One of the approaches to flood modelling is numerical simulation of the diffusive wave approximation of the shallow water equations. Improving these models in various aspects is still an open area of research. In this study, a new diffusive wave model with explicit time integration was developed which includes some novel features: (1) time steps are determined using a novel stability criterion which resulted in more dynamic time steps (i.e., broader range) compared to the conventional Courant–Friedrichs–Lewy stability condition; (2) stability constraints are reduced, considering the flow processes within surface ponds; (3) besides Manning's formula, which is the common equation for computing velocities in diffusive wave models, the free fall velocity and a new equation for wave-front velocity are employed; and (4) the influence of upstream surface ponds on downstream flow is considered. This paper introduces the enhanced diffusive wave model, the so-called Overland Flow Simulator Cellular Automata (OFS-CA), and its results for five test cases. Available analytical solutions and an experimental study were used for verification. Two other shallow water models were used for comparison and benchmarking. Overall, good agreements were observed and OFS-CA was computationally less expensive compared to the other two shallow water models.

Geometrically intrinsic modeling of shallow water flows

2020 ◽  
Vol 54 (6) ◽  
pp. 2125-2157 ◽  
Author(s):  
Elena Bachini ◽  
Mario Putti
Keyword(s):  
Shallow Water ◽  
Stokes Equations ◽  
Order Approximation ◽  
Bottom Topography ◽  
Water Model ◽  
Navier Stokes ◽  
Bottom Surface ◽  
Finite Volume Scheme ◽  
Navier Stokes Equations ◽  
Mountain Landscape

Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as a mountain landscape. In this paper we derive an intrinsic shallow water model from the Navier–Stokes equations defined on a local reference frame anchored on the bottom surface. The equations resulting are characterized by non-autonomous flux functions and source terms embodying only the geometric information. We show that the proposed model is rotational invariant, admits a conserved energy, is well-balanced, and it is formally a second order approximation of the Navier–Stokes equations with respect to a geometry-based order parameter. We then derive a numerical discretization by means of a first order upwind Godunov finite volume scheme intrinsically defined on the bottom surface. We study convergence properties of the resulting scheme both theoretically and numerically. Simulations on several synthetic test cases are used to validate the theoretical results as well as more experimental properties of the solver. The results show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures.

Comparison of 2D triangular C-grid shallow water models

2018 ◽  
Vol 161 ◽  
pp. 136-154 ◽  
Author(s):  
Hamidreza Shirkhani ◽  
Abdolmajid Mohammadian ◽  
Ousmane Seidou ◽  
Hazim Qiblawey
Keyword(s):  
Shallow Water ◽  
Shallow Water Models ◽  
Water Models

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.

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