An efficient Eulerian finite element for the shallow water equations
Hanert, E.; Le Roux, D.Y.; Legat, V.; Deleersnijder, E. (2005). An efficient Eulerian finite element for the shallow water equations. Ocean Modelling 10(1-2): 115-136. dx.doi.org/10.1016/j.ocemod.2004.06.006
In: Ocean Modelling. Elsevier: Oxford. ISSN 1463-5003; e-ISSN 1463-5011, more
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.