A characteristic mapping method for incompressible hydrodynamics on a rotating sphere
Abstract
We present a semi-Lagrangian characteristic mapping method for the incompressible Euler equations on a rotating sphere. The numerical method uses a spatio-temporal discretization of the inverse flow map generated by the Eulerian velocity as a composition of sub-interval flows formed by spherical spline interpolants. This approximation technique has the capacity of resolving sub-grid scales generated over time without increasing the spatial resolution of the computational grid. The numerical method is analyzed and validated using standard test cases yielding third-order accuracy in the supremum norm. Numerical experiments illustrating the unique resolution properties of the method are performed and demonstrate the ability to reproduce the forward energy cascade at sub-grid scales by upsampling the numerical solution.
Cite
@article{arxiv.2302.01205,
title = {A characteristic mapping method for incompressible hydrodynamics on a rotating sphere},
author = {Seth Taylor and Jean-Christophe Nave},
journal= {arXiv preprint arXiv:2302.01205},
year = {2023}
}