A Scale-Aware Anticipated Potential Vorticity Method: On Variable-Resolution Meshes

A scale-aware formulation of the anticipated potential vorticity method (APVM), previously derived for quasi-uniform unstructured grids, is evaluated on multiresolution grids. Comparison is made to the original, nonscale-aware formulation of the APVM. Numerical experiments are performed using the shallow-water standard test case 5. The scale awareness of the new formulation is demonstrated by the following obser-vations: (i) the range of optimal values for the single parameter of the new formulation is much less sensitive to grid resolution than that of the original formulation; (ii) within the optimal parameter range, the new formulation is able to maintain proper dissipation across scales and is thus able to produce better results in terms of errors in the potential enstrophy spectrum curves; and (iii) the new formulation is robust in that a single optimal parameter obtained for a specific grid can be safely used on other grids as well. 1