Casimir preserving discretization of incompressible Euler equations on S^2

The 2D Euler equations for an incompressible fluid represent a widely studied and applied model in different areas such as hydrodynamics, weather forecasts, oceanography and astrophisics. Because of this, more and more accurate numerical methods are required to solve them.
In particular, when long time simulations are required, the geometrical properties of the Euler equations play a core role in their discretization. The main property of the 2D Euler equations is their Lie-Poisson nature with an infinite number of first integrals, called Casimir functions. Here we want to present a numerical method based on the theory of quantization of Poisson algebras which gives a consistent discretization of the Euler equations on S^2, i.e., a discrete dynamics with a number of first integrals proportional to the dimension of the truncation of the exact flow. The result is remarkable since it is not achivable with a naive application of any spectral method.

Location. Room C
Schedule. 16.30-17.30