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Finite elements and finite volumes --- where to seek for the best setup

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Danilov, S. , Wang, Q. , Sidorenko, D. and Schröter, J. (2009): Finite elements and finite volumes --- where to seek for the best setup , The Eighth International Workshop on Unstructured Mesh Numerical Modelling of Coastal, Shelf and Ocean Flows, 16-18 September 2009, Louvain-la-Neuve. .
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Abstract:

We analyze obvious and less obvious advantages/difficulties,including relative numeric efficiency, of several full 3D(MPI-parallelized) setups as applied to large-scale ocean modeling.The characteristic feature of large-scale ocean circulation is thedominance of geostrophic balance and need to maintain watermassproperties on time scales spanning tens of model years. This imposeslimitation on balances, accuracy of advection schemes and numericalefficiency.On the FE side, the setups include variants of FEOM/FESOM (P1-P1prisms, P1-P1 tetrahedra, P1nc-P1 both with P1(z) and P0(z) horizontal velocity). On the FV side, there is the C-grid setup (still displaying a numerical mode if the internal Rossby radius is not properly resolved) and a setup inspired by FVCOM, but implemented for the z-coordinate, semiimplicit elevation and augmented with several variants of dissipation operators(biharmonic and modified Leith) that keep the code stable at relatively high grid Reynolds numbers. All FEOM variants show nearly equal CPU efficiency. The numerical efficiency suggested by the FVCOM-like approach exceeds that of FEOM by a factor of 5, being not worse than that of the C-grid approach. Its downside as applied to large-scale ocean modeling tasks is the need in better advection schemes that show less numerical dissipation. Questions that seem important to us on the technical side continue to include the numerical efficiency (data structure and solvers adapted to specific tasks). On the physical side, the question of minimizing spurious diapycnal mixing accompanying advection on unstructured meshes gains in importance as model integration time is increased.

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21409
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