An efficient Eulerian finite element method for the shallow water equations

The accuracy and efficiency of an Eulerian method is assessed by solving the non-linear shallow water equations and compared with the performances of an existing semi-Lagrangian method. Both methods use a linear non-conforming finite element discretization for velocity and a linear conforming finite...

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Bibliographic Details
Published in:Ocean modelling (Oxford) 2005, Vol.10 (1), p.115-136
Main Authors: Hanert, Emmanuel, Roux, Daniel Y. Le, Legat, Vincent, Deleersnijder, Eric
Format: Article
Language:English
Subjects:
Euleurian
Finite elements
Kriging
Non-conforming linear interpolation
Rossby waves
Semi-Lagrangian
Shallow water equations
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Summary:The accuracy and efficiency of an Eulerian method is assessed by solving the non-linear shallow water equations and compared with the performances of an existing semi-Lagrangian method. Both methods use a linear non-conforming finite element discretization for velocity and a linear conforming finite element discretization for surface elevation. This finite element pair is known to be computationally efficient and free of pressure modes. The model equations are carefully derived and a comparison is performed by simulating the propagation of slow Rossby waves in the Gulf of Mexico. Simulations show that the Eulerian model performs well and gives results comparable to high order semi-Lagrangian schemes using kriging interpolators.
ISSN:1463-5003
1463-5011
DOI:10.1016/j.ocemod.2004.06.006