Variational integrators for soundproof models on arbitrary triangular C-grids

Werner Bauer 1, 2, 3 François Gay-Balmaz 3
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : We introduce variational integrators for soundproof approximations of the Euler equations on irregular triangular C-grids. In particular we provide explicit vector-matrix formulations and the solving algorithm for the previously derived discrete covariant equations of Boussinesq, anelastic, and pseudo-incompressible models of [4]. The derivation of these variational integrators is based on a discrete version of the Euler-Poincaré variational method, hence it provides structure-preserving discretizations that preserve Kelvin's circulation theorem and provide excellent long term energy behavior for arbitrary triangular C-grids. We verify the structure-preserving nature of these schemes for various scenarios of geophysical relevance: the hydrostatic adjustment process, the Kelvin-Helmholtz instability, and the cold and warm bubble test cases.
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Werner Bauer, François Gay-Balmaz. Variational integrators for soundproof models on arbitrary triangular C-grids. 2019. ⟨hal-01970335⟩

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