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

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-Poincare reduction framework for Eulerian hydrodynamics. We describe the discretization of the continuous Euler-Poincare 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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