A CHEBYSHEV PROJECTION METHOD FOR SOLVING SHALLOW-WATER EQUATIONS

2021 ◽  
Vol 10 (11) ◽  
pp. 3461-3477
Author(s):  
Y.A. Mahaman Nouri ◽  
S. Bisso
Keyword(s):  
Shallow Water ◽  
Projection Method ◽  
Shallow Water Equations ◽  
Numerical Approach ◽  
Spectral Approach ◽  
Projection Technique ◽  
Water Flows ◽  
Collocation Points ◽  
2D Shallow Water Equations

The aims of this paper is to propose a numerical approach to simulate water flows in a 2D shallow medium. We consider the 2D Shallow water equations following the velocity-denivelation formulation. We solve these equations by a projection technique using a $\mathbb{P}_{N,M}$-type Chebyshev spectral approach which uses the Chebyshev-Gauss-Lobatto collocation points.

scholarly journals Urban Flood Modeling Using 2D Shallow-Water Equations in Ouagadougou, Burkina Faso

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2120
Author(s):  
Gnenakantanhan Coulibaly ◽  
Babacar Leye ◽  
Fowe Tazen ◽  
Lawani Adjadi Mounirou ◽  
Harouna Karambiri
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Urban Areas ◽  
Flood Hazard ◽  
Scientific Information ◽  
Roughness Coefficient ◽  
Flood Events ◽  
African Countries ◽  
Numerical Tool ◽  
2D Shallow Water Equations

Appropriate methods and tools accessibility for bi-dimensional flow simulation leads to their weak use for floods assessment and forecasting in West African countries, particularly in urban areas where huge losses of life and property are recorded. To mitigate flood risks or to elaborate flood adaptation strategies, there is a need for scientific information on flood events. This paper focuses on a numerical tool developed for urban inundation extent simulation due to extreme tropical rainfall in Ouagadougou city. Two-dimensional (2D) shallow-water equations are solved using a finite volume method with a Harten, Lax, Van Leer (HLL) numerical fluxes approach. The Digital Elevation Model provided by NASA’s Shuttle Radar Topography Mission (SRTM) was used as the main input of the model. The results have shown the capability of the numerical tool developed to simulate flow depths in natural watercourses. The sensitivity of the model to rainfall intensity and soil roughness coefficient was highlighted through flood spatial extent and water depth at the outlet of the watershed. The performance of the model was assessed through the simulation of two flood events, with satisfactory values of the Nash–Sutcliffe criterion of 0.61 and 0.69. The study is expected to be useful for flood managers and decision makers in assessing flood hazard and vulnerability.

scholarly journals Inverse algorithms for 2D shallow water equations in presence of wet dry fronts: Application to flood plain dynamics

2016 ◽  
Vol 97 ◽  
pp. 11-24 ◽  
Author(s):  
J. Monnier ◽  
F. Couderc ◽  
D. Dartus ◽  
K. Larnier ◽  
R. Madec ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Flood Plain ◽  
2D Shallow Water Equations

scholarly journals Weak Local Residuals as Smoothness Indicators in Adaptive Mesh Methods for Shallow Water Flows

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 345
Author(s):  
Sudi Mungkasi ◽  
Stephen Gwyn Roberts
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Adaptive Mesh ◽  
Finite Volume Methods ◽  
Water Type ◽  
Two Dimensional ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Smoothness Indicators

This paper proposes some formulations of weak local residuals of shallow-water-type equations, namely, one-, one-and-a-half-, and two-dimensional shallow water equations. Smooth parts of numerical solutions have small absolute values of weak local residuals. Rougher parts of numerical solutions have larger absolute values of weak local residuals. This behaviour enables the weak local residuals to detect parts of numerical solutions which are smooth and rough (non-smooth). Weak local residuals that we formulate are implemented successfully as refinement or coarsening indicators for adaptive mesh finite volume methods used to solve shallow water equations.

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