Accurate prediction of hurricane tracks may require resolving the flow both within and around the storm. Since the spatial scales in these two regions differ substantially, uniform resolution is inherently inefficient: the grid should be refined only near the storm. An adaptive multigrid barotropic model (MUDBAR) which does this has been described previously. Based on the nondivergent barotropic vorticity equation, this model uses an adaptive multigrid scheme to refine the mesh only around the moving storm.
This paper describes and evaluates improvements to the MUDBAR model. We concentrate on the solution algorithm, focusing on the method of Berger and Oliger (which uses only local coarse grids) and the method of Bai and Brandt (which uses full coarse grids with FAS processing). We also plan to treat the FAC method. Preliminary results show significant differences in accuracy between these methods; however, these differences are small compared to the savings of simply using nonuniform resolution. For this problem, conservation of energy, vorticity, and enstrophy is crucial; conservation properties of the various methods will be compared. Finally, we investigate the performance of a fully self-adaptive version of the model, using estimates of the local truncation error obtained during multigrid processing to control where to refine or coarsen the grid.