Explicit, parallel Poisson integration of point vortices on the sphere

Solutions to ideal fluid flow where the vorticity field is assumed as a sum of singular point vortices result in a Poisson system describing the motion of the vortex centres. We construct Poisson integration methods for these dynamics by splitting the Hamiltonian into its constituent vortex pair terms. From backward error analysis, the method is formally known to provide solutions to a modified Poisson system with the correct bracket, but with a modified Hamiltonian function. Different orderings of the pairwise interactions are considered and also used for the construction of higher order methods. The energy and momentum conservation of the splitting schemes is demonstrated for several test cases. For particular orderings of the pairwise interactions, the schemes allow scalable parallelization. This results in a linear – as opposed to quadratic – scaling of computation time with system size when scaling the number of processors accordingly.