Regularising subgrid scale information in the next generation of ocean models
A. Candy, C. Pain, M. Piggott, D. Ham
Department of Earth Science and Engineering, Imperial College London, UK (adam.candy@imperial.ac.uk; http://amcg.ese.ic.ac.uk/~adam)

A consideration of stabilisation techniques is essential in ocean
model development if finite element-based models are to correctly model
ocean processes over a wide-range of scales.  Careful application of
these techniques can significantly increase flexibility of models and
allow meshes to become highly anisotropic.  This enables the model to
capture a wider range of ocean phenomena and thus reduce the number
of parameterisations required, bringing us a more physically realistic
solution.

The next generation of ocean models employ unstructured meshes and
anisotropic adaptivity to gain a greater degree of flexibility.
These however, also introduce erroneous artefacts into the solution,
when for example a process becomes unresolvable due to an adaptive mesh
change or advection into a coarser resolution of mesh in the domain.
The suppression of these effects, caused by spatial and temporal
variations in mesh size, is one of the key roles stabilisation can play.

In this presentation, we will discuss a range of stabilisation
techniques suitable for application in ocean modelling.  We will compare
traditional schemes such as Petrov-Galerkin and Galerkin least-squares
with more recently developed schemes derived from subgrid scale modelling
concepts for advection-diffusion processes.  With a focus on consistent
and residual-free schemes we will discuss the application of the
variational multiscale method, residual-free bubble function enrichment,
a newly-developed fourth-order scheme and a new subgrid scale model in
our aim to capture the important fine-scale information.

In combination with adaptive methods, stabilising techniques are key to
the development of next generation ocean models.  In particular, these
ideas are critical if we are to achieve our aim of extending models,
such as the Imperial College Ocean Model, to the global-scale.