What the study found
The study found that stability limits for divergence and vorticity damping on gnomonic cubed-sphere grids vary with the grid mapping. The limits depend on cell areas, aspect ratios, and grid nonorthogonality, and practical vorticity limits in FV3 are lower than the explicit stability limits.
Why the authors say this matters
The authors state that divergence and vorticity damping are used to maintain stability in dynamical cores, so knowing their mesh-dependent upper bounds helps avoid numerical blow-up from overly strong diffusion. The study suggests these limits are relevant for choosing damping coefficients on cubed-sphere grids and for understanding how the horizontal transport scheme affects vorticity damping.
What the researchers tested
The researchers derived stability limits using von Neumann analysis, a linear method for testing whether numerical schemes remain stable, for three gnomonic cubed-sphere meshes: equidistant, equiangular, and equi-edge. They examined damping with a simplified pseudo-Laplacian operator, as used in NOAA GFDL’s FV3 finite-volume dynamical core, and with the full curvilinear Laplacian. They also compared the analytical limits with practical upper bounds from idealized tests on the equiangular and equi-edge grids.
What worked and what didn't
For divergence damping, the maximum stable coefficients and the locations where instability appeared agreed with linear theory. For vorticity damping, practical limits were lower than the explicit stability limits because of implicit vorticity diffusion in the FV3 transport scheme, and those limits depended on the horizontal transport scheme. The stability limits changed across the three grid mappings.
What to keep in mind
The abstract does not describe detailed limitations beyond the dependence on grid type and transport scheme. The practical comparisons were reported for the equiangular and equi-edge grids, so the abstract does not say whether the same practical tests were done for the equidistant grid.
Key points
- Divergence and vorticity damping have mesh-dependent stability limits on gnomonic cubed-sphere grids.
- The limits depend on cell areas, aspect ratios, and grid nonorthogonality.
- For divergence damping, practical behavior matched linear stability theory.
- For vorticity damping, practical limits in FV3 were lower than explicit stability limits.
- The vorticity limits also depended on the horizontal transport scheme.
Disclosure
- Research title:
- Stability limits for damping depend on cubed-sphere grid choice
- Image credit:
- Photo by ChiemSeherin on Pixabay
Get the weekly research newsletter
Stay current with peer-reviewed research without reading academic papers — one filtered digest, every Friday.