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| Titel |
A mixed discontinuous/continuous finite element pair for geophysical flows |
| VerfasserIn |
C. J. Cotter, D. A. Ham, C. C. Pain, S. Reich |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250026584
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| Zusammenfassung |
| The Imperial College Ocean Model (ICOM) is an advanced
three-dimensional, non-hydrostatic adaptive mesh ocean model which
includes advances developed in the sphere of industrial fluid
mechanics. However, large-scale flows in the atmosphere and ocean
remain in a state of slow evolution called geostrophic balance in
which fast oscillations are very weak; these slowly-evolving dynamical
states represent our weather and the global circulation patterns. To
make predictions on these scales, special care must be taken to design
numerical methods which reflect the properties of this underlying
balance. This calls for new discretisation methods which reflect
geostrophic balance. We introduce a new family of mixed finite element
methods which combine discontinuous and continuous elements in a new
way to produce a stable discretisation which provides the best
possible representation of geostrophic balance on unstructured
meshes. The proofs of these properties are very simple since they are
based on underlying geometric structure: the discretisations have
exact sequences which mimic the div-curl and curl-grad relations of
vector analysis. We demonstrate that the element exactly preserves
geostrophic balance in the shallow water equations and provides an
excellent representation of density-driven instabilities even at very
low resolution. |
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