High-resolution, monotone solution of the adjoint shallow-water equations

2002 ◽  
Vol 38 (2) ◽  
pp. 139-161 ◽  
Author(s):  
Brett F. Sanders ◽  
Scott F. Bradford
Keyword(s):  
High Resolution ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Monotone Solution

Application of the TELEMAC-2D Model in the Fluvial Hydrodinamics Simulation and Reproduction of Flood Patterns

2019 ◽  
Vol 396 ◽  
pp. 187-196
Author(s):  
Aldair Forster ◽  
Juliana Costi ◽  
Wiliam Correa Marques ◽  
André Gustavo Wormsbecher ◽  
Antonio Raylton Rodrigues Bendo
Keyword(s):  
Finite Element ◽  
High Resolution ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Models ◽  
Finite Element Mesh ◽  
Element Mesh ◽  
The City ◽  
2D Model ◽  
National Water

. The increased occurrence of floods in the city of Rio do Sul (SC), even with the creation of dams to contain floods, show that non-structural measures can be good alternatives to reduce losses in the region. Numerical flood modeling has been widely used to anticipate risks and assist in decisionmaking. One of the numerical models that is being used to simulate floods is TELEMAC-2D, which is able to simulate the hydrodynamics of open channels by solving the shallow water equations in a domain discretized by an unstructured finite element mesh. We used the TELEMAC-2D model tosimulate the dynamics of the rivers of the region of Rio do Sul throughout the year of 2013, period during which a flood with large proportions occurred in September. Fluviometric data avaliable from the National Water Agency and high resolution (1 m) topographic data provided by government agen-cies of Santa Catarina were used in the simulation. The results show that the model performed well in simulating the maximum flood extension occurred in September, however, the simulations were underestimated for most of the time, indicating that calibrations in the model can still be performed.

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.

MAPPING TIDAL CURRENTS AND RESIDUAL CURRENTS BY USE OF COASTAL ACOUSTIC TOMOGRAPHY

2017 ◽  
Author(s):  
Xiao-Hua Zhu ◽  
Xiao-Hua Zhu ◽  
Ze-Nan Zhu ◽  
Ze-Nan Zhu ◽  
Xinyu Guo ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Mean Amplitude ◽  
Momentum Equation ◽  
Tidal Currents ◽  
Acoustic Tomography ◽  
Mean Values ◽  
Residual Currents ◽  
Water Depths ◽  
Deep Area

A coastal acoustic tomography (CAT) experiment for mapping the tidal currents in the Zhitouyang Bay was successfully carried out with seven acoustic stations during July 12 to 13, 2009. The horizontal distributions of tidal current in the tomography domain are calculated by the inverse analysis in which the travel time differences for sound traveling reciprocally are used as data. Spatial mean amplitude ratios M2 : M4 : M6 are 1.00 : 0.15 : 0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, velocity amplitudes of M4 measured by CAT agree well with those of M4 predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area where water depths are larger than 60 m is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. Dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents.

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