Ocean modeling on unstructured meshes

- We review approaches to large-scale unstructured-mesh ocean circulation modeling.
- Most of proposed discretizations on triangular or hexagonal unstructured meshes suffer from spurious modes.
- Large velocity space requires efficient filtering of small scales.
- Hexagonal C-grid and triangular cell-vertex finite-volume discretizations can be recommended.

Unstructured meshes are common in coastal modeling, but still rarely used for modeling the large-scale ocean circulation. Existing and new projects aim at changing this situation by proposing models enabling a regional focus (multiresolution) in global setups, without nesting and open boundaries. Among them, finite-volume models using the C-grid discretization on Voronoi-centroidal meshes or cell-vertex quasi-B-grid discretization on triangular meshes work well and offer the multiresolution functionality at a price of being 2 to 4 times slower per degree of freedom than structured-mesh models. This is already sufficient for many practical tasks and will be further improved as the number of vertical layers is increased. Approaches based on the finite-element method, both used or proposed, are as a rule slower at present. Most of staggered discretizations on triangular or Voronoi meshes allow spurious modes which are difficult to filter on unstructured meshes. The ongoing research seeks how to handle them and explores new approaches where such modes are absent. Issues of numerical efficiency and accurate transport schemes are still important, and the question on parameterizations for multiresolution meshes is hardly explored at all. The review summarizes recent developments the main practical result of which is the emergence of multiresolution models for simulating large-scale ocean circulation.