Session A5 - Geometric Integration and Computational Mechanics
July 12, 15:30 ~ 16:00 - Room 111
Variational integrators in geophysical fluid dynamics
CNRS & Ecole Normale Supérieure de Paris, France - email@example.com
We present an overview of structure-preserving variational discretizations of various equations of geophysical fluid dynamics, such as the anelastic, pseudo-incompressible, and shallow-water equations. These discretizations rely on finite dimensional approximations of the groups of diffeomorphisms underlying the dynamics. In particular, we extend previous approches to the compressible case. As descending from variational principles, the discussed variational schemes exhibit discrete versions of Kelvin circulation theorems, are applicable to irregular meshes, and show excellent long term energy behavior.
Joint work with Werner Bauer (Imperial College, London).