Comparison of mesh-adaptation criteria for an idealized tropical cyclone problem

Abstract

The development and motion of tropical cyclones is influenced by processes on a wide range of scales.
Adaptive meshes are a promising way to reduce the computational costs of numerical simulations for
such multiscale problems. Mesh adaptation can be controlled by various criteria for which cell-wise
indicators are typically introduced. We analyze indicators based on a posteriori error estimators, goal-
oriented error estimators, and physical criteria. To compare these different approaches, we propose
indicators for physical quantities formulated in a way that allows us to apply the same mesh adaptation
strategy to all cases. As a benchmark problem we investigate the interaction of two tropical cyclones
in an idealized framework. On adaptive meshes, the track prediction error could be reduced up to
two orders of magnitude compared to uniform meshes. We describe the costs for the computational
evaluation of the investigated indicators and discuss the efficiency of the resulting adaptive methods.