Accurate prediction of tropical cyclone 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. The success of conventional nested-grid models (e.g., GFDL, VICBAR) demonstrates the value of this approach.
The multigrid barotropic model (MUDBAR) described here takes this idea one step farther: in addition to superimposing uniform grids of different mesh sizes and spatial extent to produce local mesh refinement, the interplay between the grids where they overlap is used to accelerate the solution process. Two-way interaction at the grid interfaces allows the fine-grid solution to immediately affect the coarse-grid solution, resulting in a seamless representation of the flow on all grids and scales.
Preliminary versions of the model described previously used grid patches of fixed size which moved with the vortex. In this paper we introduce a fully self-adaptive version, using accurate truncation error estimates computed during multigrid processing to determine where to refine or coarsen the grids as the solution evolves. In addition, the error estimates can be used to obtain fourth-order accuracy from the second-order discretization via an extrapolation process with little additional work.
The paper will focus on two main areas: describing the key aspects of the self-adaptive multigrid method and quantifying its performance. In particular, we will investigate the trade-off between accuracy and efficiency, the sensitivity of the model performance to various control parameters, gains produced by extrapolation to higher-order accuracy, and the benefit of self-adaptivity as compared to using fixed patch sizes. In addition, we will use the model to investigate the sensitivity of tropical cyclone tracks to vortex size, intensity, and structure and to model resolution