This paper describes how to solve the incompressible Euler equations in spherical coordinates on a staggered grid defined on the sphere. The goal of this method is to accurately model fluid behavior regardless of the underlying grid definition (i.e, the result should be grid-agnostic). In particular, we invent and implement several techniques to manage polar singularities that emerge in the spherical coordinate representation of the incompressible Euler equations.
This work is published in Proceedings of the ACM (PACM), and can be downloaded here. My colleague Bowen Yang and I are co-first authors on the paper.
I presented this work at the I3D conference in Montreal in 2019. The slides can be downloaded here. If you have keynote, the presentation (with demos) can be downloaded here.
This project lives on GitHub and can be downloaded here.
Advised by Professor Chenfanfu Jiang at the University of Pennsylvania.