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Journal Articles Quarterly Journal of the Royal Meteorological Society Year : 2019

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

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.

Dates and versions

hal-02414164 , version 1 (16-12-2019)

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Rüdiger Brecht, Werner Bauer, Alexander Bihlo, François Gay-Balmaz, Scott Maclachlan. Variational integrator for the rotating shallow‐water equations on the sphere. Quarterly Journal of the Royal Meteorological Society, 2019, 145 (720), pp.1070-1088. ⟨10.1002/qj.3477⟩. ⟨hal-02414164⟩
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