Skip to main content

IMIS

A new integrated search interface will become available in the next phase of marineinfo.org.
For the time being, please use IMIS to search available data

 

[ report an error in this record ]basket (0): add | show Print this page

A finite element method for solving the shallow water equations on the sphere
Comblen, R.; Legrand, S.; Deleersnijder, E.; Legat, V. (2009). A finite element method for solving the shallow water equations on the sphere. Ocean Modelling 28(1-3): 12-23. dx.doi.org/10.1016/j.ocemod.2008.05.004
In: Ocean Modelling. Elsevier: Oxford. ISSN 1463-5003; e-ISSN 1463-5011, more
Peer reviewed article  

Available in  Authors 

Author keywords
    Curved manifolds; Finite element; Shallow water equations; Spherical

Authors  Top 

Abstract
    Within the framework of ocean general circulation modeling, the present paper describes an efficient way to discretize partial differential equations on curved surfaces by means of the finite element method on triangular meshes. Our approach benefits from the inherent flexibility of the finite element method. The key idea consists in a dialog between a local coordinate system defined for each element in which integration takes place, and a nodal coordinate system in which all local contributions related to a vectorial degree of freedom are assembled. Since each element of the mesh and each degree of freedom are treated in the same way, the so-called pole singularity issue is fully circumvented.
    Applied to the shallow water equations expressed in primitive variables, this new approach has been validated against the standard test set defined by [Williamson, D.L., Drake, J.B., Hack, J.J., Jakob, R., Swarztrauber, P.N., 1992. A standard test set for numerical approximations to the shallow water equations in spherical geometry. journal of Computational Physics 102, 211-224]. Optimal rates of convergence for the P1NC - P1 finite element pair are obtained, for both global and local quantities of interest. Finally, the approach can be extended to three-dimensional thin-layer flows in a straightforward manner.

All data in the Integrated Marine Information System (IMIS) is subject to the VLIZ privacy policy Top | Authors