A comparison of 4 advection schemes for use in unstructured grid ocean modelling
Hanert, E.; Le Roux, D.Y.; Legat, V.; Deleersnijder, E. (2003). A comparison of 4 advection schemes for use in unstructured grid ocean modelling, in: 6th National Congress on Theoretical and Applied Mechanics, Ghent, May 26-27, 2003. pp. 1-8
In: (2003). 6th National Congress on Theoretical and Applied Mechanics, Ghent, May 26-27, 2003. Nationaal Comité voor Theoretische en Toegepaste Mechanica: Gent. 1 cd pp., more
We study advection schemes for unstructured grid ocean models. Four linear advection schemes are investigated by solving a scalar transport equation. Schemes under consideration include continuous, non-conforming and discontinuous finite elements and finite volumes. A comprehensive derivation of the numerical schemes is presented and dispersion and conservation properties are discussed. An assessment is made by performing the test problem introduced by Hecht et al. [J. Geophys. Res. 100 (1995) 20763-20778] in which a passive scalar field is advected through an analytical Stommel gyre. It is found that continuous finite elements and finite volumes have some difficulties to represent accurately solutions with steep gradients. As a result they are prone to generate unphysical oscillations. On the other hand, discontinuous and non-conforming finite element schemes perform better. This is due to their higher flexibility that makes them better suited to highly sheared flows.
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