Title
Using Power diagrams to build optimal unstructured meshes for C-grid models
Authors
Darren Engwirda (Unlicensed), Columbia University
Xylar Asay-Davis, LANL
Mark Petersen, LANL
Phillip Wolfram (Unlicensed), LANL
Steven Brus, LANL
Kristin Hoch (Unlicensed), LANL
Mike Herzfeld, CSIRO
Farhan Rizwi, CSIRO
Abstract
Can we do better than Voronoi diagrams when building unstructured meshes for C-grid GCMs? By exploring the relationship between discretisation error and mesh layout, a new unstructured meshing kernel is proposed for the generation of 'weighted', 'Voronoi-like' configurations known as 'Power diagrams'. Seeking to minimise errors in the discrete numerical operators, a 'primal-dual' optimisation strategy is derived to compute the vertex positions, weights and cell topology of a given variable-resolution mesh. These optimised 'Power' meshes are shown to improve grid geometry and reduce staggering errors. These improvements are especially useful for difficult cases incorporating aggressive changes in resolution and user-defined constraints such as coastlines.