Stability of some exact solutions of the shallow-water equations for testing numerical models in spherical geometry

2008 ◽  
Vol 134 (632) ◽  
pp. 771-778 ◽  
Author(s):  
A. Staniforth ◽  
A. A. White
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Models ◽  
Spherical Geometry

scholarly journals Approximate Traveling Wave Solutions of Coupled Whitham-Broer-Kaup Shallow Water Equations by Homotopy Analysis Method

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
M. M. Rashidi ◽  
D. D. Ganji ◽  
S. Dinarvand
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Homotopy Analysis Method ◽  
Shallow Water Equations ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Analysis Method ◽  
Wave Solutions ◽  
Homotopy Analysis

The homotopy analysis method (HAM) is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup (WBK) equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.

scholarly journals Symmetries and exact solutions of the rotating shallow-water equations

2009 ◽  
Vol 20 (5) ◽  
pp. 461-477 ◽  
Author(s):  
A. A. CHESNOKOV
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
New Class ◽  
New Exact Solutions ◽  
Time Periodic Solutions ◽  
Rotating Shallow Water ◽  
Rotating Shallow Water Equations ◽  
Time Periodic

Lie symmetry analysis is applied to study the non-linear rotating shallow-water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow-water equations can be transformed to the classical shallow-water model. The derived symmetries are used to generate new exact solutions of the rotating shallow-water equations. In particular, a new class of time-periodic solutions with quasi-closed particle trajectories is constructed and studied. The symmetry reduction method is also used to obtain some invariant solutions of the model. Examples of these solutions are presented with a brief physical interpretation.

Computational study of some nonlinear shallow water equations

Open Physics ◽  
2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Ali Bhrawy ◽  
Mohamed Abdelkawy
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Periodic Solutions ◽  
Shallow Water Equations ◽  
Computational Study ◽  
Expansion Method ◽  
Coastal Areas ◽  
Atmospheric Modeling ◽  
Hydraulic Engineering ◽  
Nonlinear Shallow Water Equations

AbstractThe shallow water equations have wide applications in ocean, atmospheric modeling and hydraulic engineering, also they can be used to model flows in rivers and coastal areas. In this article we obtained exact solutions of three equations of shallow water by using $\frac{{G'}} {G} $-expansion method. Hyperbolic and triangular periodic solutions can be obtained from the $\frac{{G'}} {G} $-expansion method.

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.

A standard test set for numerical approximations to the shallow water equations in spherical geometry

1992 ◽  
Vol 101 (1) ◽  
pp. 227-228 ◽  
Author(s):  
David L Williamson ◽  
John B Drake ◽  
James J Hack ◽  
Rüdiger Jakob ◽  
Paul N Swarztrauber
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Spherical Geometry ◽  
Standard Test ◽  
Numerical Approximations ◽  
Test Set
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