Numerical Schemes for 2D Shallow Water Equations with Variable Depth and Friction Effects

2003 ◽  
pp. 506-511
Author(s):  
Tomás Chacón Rebollo ◽  
Antonio Domínguez Delgado ◽  
Enrique D. Fernández Nieto
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Variable Depth ◽  
Numerical Schemes ◽  
2D Shallow Water Equations

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 Convergence Improved Lax-Friedrichs Scheme Based Numerical Schemes and Their Applications in Solving the One-Layer and Two-Layer Shallow-Water Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Xinhua Lu ◽  
Bingjiang Dong ◽  
Bing Mao ◽  
Xiaofeng Zhang
Keyword(s):  
High Resolution ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Small Time ◽  
Numerical Schemes ◽  
Time Step ◽  
Numerical Diffusion ◽  
First Order ◽  
Small Time Step ◽  
The One

The first-order Lax-Friedrichs (LF) scheme is commonly used in conjunction with other schemes to achieve monotone and stable properties with lower numerical diffusion. Nevertheless, the LF scheme and the schemes devised based on it, for example, the first-order centered (FORCE) and the slope-limited centered (SLIC) schemes, cannot achieve a time-step-independence solution due to the excessive numerical diffusion at a small time step. In this work, two time-step-convergence improved schemes, the C-FORCE and C-SLIC schemes, are proposed to resolve this problem. The performance of the proposed schemes is validated in solving the one-layer and two-layer shallow-water equations, verifying their capabilities in attaining time-step-independence solutions and showing robustness of them in resolving discontinuities with high-resolution.

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