Variational integrator for the rotating shallow-water equations on the sphere
Numerical Analysis
2019-02-25 v2 Atmospheric and Oceanic Physics
Abstract
We develop a variational integrator for the shallow-water equations on a rotating sphere. The variational integrator is built around a discretization of the continuous Euler-Poincar\'{e} reduction framework for Eulerian hydrodynamics. We describe the discretization of the continuous Euler-Poincar\'{e} equations on arbitrary simplicial meshes. Standard numerical tests are carried out to verify the accuracy and the excellent conservational properties of the discrete variational integrator.
Cite
@article{arxiv.1808.10507,
title = {Variational integrator for the rotating shallow-water equations on the sphere},
author = {Rüdiger Brecht and Werner Bauer and Alexander Bihlo and François Gay-Balmaz and Scott MacLachlan},
journal= {arXiv preprint arXiv:1808.10507},
year = {2019}
}