| Abstract: |
| Unstructured meshes have been gaining popularity in recent years,
because they are almost free of polar singularities, and remain highly
scalable even at eddy resolving resolutions. However, to unleash the
full potential of these meshes, new schemes are needed. The
classical C-grid scheme, which is widely popular on structured meshes,
has serious issues concerning the reconstruction of the tangential
velocity component. This talk presents new numerical schemes based on
an old idea, namely the collocated vorticity-divergence formulation
(so-called Z-grid), for large-scale geophysical flows on unstructured
centroidal Voronoi meshes. Using the finite-volume discretization
technique, the schemes conserve the mass and the absolute vorticity
locally, and the potential enstrophy globally. It is also shown that,
in an area-averaged sense, the schemes reproduce the Lagrangian
transport property for potential vorticity, which is fundamental to
the understanding of the dynamics of large-scale geophysical flows. A
major challenge of vorticity-divergence based numerical schemes is the
specification of the boundary conditions for the PDEs. This project
adopts a hybrid approach that combines explicit and implicit
implementation of the boundary conditions on the streamfunction and
velocity potential. This talk will go over the analytical and
practical aspects of the schemes, and finish with some high-resolution
numerical results. |
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