A coastal unstructured model using Voronoi meshes and C-grid staggering

Abstract

A coastal ocean model is presented, adapting the unstructured C-grid discretisation (Ringler et al., 2010) employed in the MPAS (Model for Prediction Across Scales) global ocean model for use in an existing structured coastal modelling framework. Specifically, the discretisation of momentum advection, horizontal viscosity, Coriolis and continuity due to Ringler et al. are used; remaining terms are adapted from their equivalent formulations on structured meshes. The new model operates on an unstructured variant of the Arakawa C-grid, whereby normal velocity components are staggered at the edges of Voronoi cells, with fluid height and tracer variables located at cell centres. In contrast to equivalent C-grid formulations on triangular meshes, there is no requirement to suppress spurious numerical modes associated with the horizontal divergence operator, alleviating a significant difficulty often associated with unstructured C-grid models. Additional attention was required to make the new model applicable to coastal configurations, vis. open boundaries, wetting and drying and inline meshing capabilities. Extensions of existing high-order tracer advection schemes were also implemented to operate on Voronoi-type meshes. The model was tested in a realistic application (a flood event in a complex coastal embayment) subject to full forcing which exercised these unstructured numerics. Model solutions compared favourably to observations collected from a Slocum glider, tide gauge and sub-surface mooring.