An initial-value problem for testing numerical models of the global shallow-water equations

2004 ◽  
Vol 56 (5) ◽  
pp. 429-440 ◽  
Author(s):  
JOSEPH GALEWSKY ◽  
RICHARD K. SCOTT ◽  
LORENZO M. POLVANI
Keyword(s):  
Shallow Water ◽  
Initial Value Problem ◽  
Shallow Water Equations ◽  
Numerical Models ◽  
Initial Value

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 Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods – Part 1: Derivation and properties

2017 ◽  
Vol 10 (2) ◽  
pp. 791-810 ◽  
Author(s):  
Christopher Eldred ◽  
David Randall
Keyword(s):  
Total Energy ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Models ◽  
Standard Test ◽  
Exterior Calculus ◽  
Hamiltonian Methods ◽  
Discrete Analogues ◽  
Work Done ◽  
Potential Enstrophy

Abstract. The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.

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