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arXiv · 1808.10507

Variational integrator for the rotating shallow-water equations on the sphere

Rüdiger Brecht·Werner Bauer·Alexander Bihlo·François Gay-Balmaz·Scott MacLachlan
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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.

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Rüdiger Brecht, Werner Bauer, Alexander Bihlo, François Gay-Balmaz, Scott MacLachlan. 2018-08-30. Variational integrator for the rotating shallow-water equations on the sphere. https://doi.org/10.1002/qj.3477

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