Georgia Institute of Technology College of Sciences

Large-scale geophysical flows, i.e. the ocean and atmosphere, evolve on spatial scales ranging from meters to thousands of kilometers, and on temporal scales ranging from seconds to decades. These scales interact in a highly nonlinear fashion, making it extremely challenging to reliably and accurately capture the long-term dynamics of these flows on numerical models. In fact, this problem is closely associated with the grand challenges of long-term weather and climate predictions. Unstructured meshes have been gaining popularity in recent years on geophysical models, thanks to its being almost free of polar singularities, and remaining highly scalable even at eddy resolving resolutions. However, to unleash the full potential of these meshes, new schemes are needed. This talk starts with a brief introduction to large-scale geophysical flows. Then it goes over the main considerations, i.e. various numerical and algorithmic choices, that one needs to make in deisgning numerical schemes for these flows. Finally, a new vorticity-divergence based finite volume scheme will be introduced. Its strength and challenges, together with some numerical results, will be presented and discussed.