Evaluation of the utility of static and adaptive mesh refinement for idealized tropical cyclone problems in a spectral element shallow-water model

The utility of static and adaptive mesh refinement (SMR and AMR, respectively) are examined for idealized tropical cyclone (TC) simulations in a two-dimensional spectral element f-plane shallow-water model. The SMR simulations have varying sizes of the statically refined meshes (geometry based) while the AMR simulations use a potential vorticity (PV) threshold to adaptively refine the mesh to the evolving TC. Numerical simulations are conducted for four cases: (i) TC-like vortex advecting in a uniform flow, (ii) binary vortex interaction, (iii) barotropic instability of a PV ring, and (iv) barotropic instability of a thin strip of PV. For each case, a uniform grid high-resolution "truth" simulation is compared to two different SMR simulations and three different AMR simulations for accuracy and efficiency. The multiple SMR and AMR simulations have variations in the number of fully refined elements in the vicinity of the TC. For these idealized cases, it is found that the SMR and AMR simulations are able to resolve the vortex dynamical processes (e.g., barotropic instability, Rossby wave breaking, and filamentation) as well as the truth simulations, with no significant loss in accuracy in the refined region in the vortex vicinity and with significant speedups (factors of 4-15, depending on the total number of refined elements). The overall accuracy is enhanced by a greater area of fully refined mesh in both the SMR and AMR simulations.