Dear all,

You are all invited to the following NOMADS seminar by Paolo Cifani, GSSI, which will take place Today at 13:45 in MLH and online via zoom at the following address: https://us02web.zoom.us/j/83830006962?pwd=SmI1MTVKRTllU3dBR01Ybko5bzBJdz09 https://us02web.zoom.us/j/83830006962?pwd=SmI1MTVKRTllU3dBR01Ybko5bzBJdz09

Looking forward to seeing you all later!

Nicola and Francesco

============== GSSI, via F Crispi 7. Room: MLH. Date: 24 May at 13:45

Paolo Cifani (GSSI)

Geometric integration of Lie-Poisson flows on the sphere

In this seminar I will touch upon the recent developments in structure-preserving (geometric) integration of Euler’s equations for two-dimensional incompressible flows. It has been known for half a century that the dynamics of incompressible ideal fluids in two dimensions can be understood as an evolution equation on the contangent bundle of the infinite-dimensional Lie group of symplectic dffeomorphisms. In particular, the vorticity equation constitutes a Lie-Poisson system characterized by an infinite number of first integrals, i.e. the integrated powers of vorticity. This set of constraints, absent in three dimensions, has profound effects on the energy transfer mechanisms across scales of motion. Yet, the construction of a numerical system which preserves this rich Poisson structure has been elusive. Most attempts either fail in fully preserving the geometric structure or have a high computational complexity. Here, I will show that, thanks to our recent advances, it possible to design a geometric integrator which embeds this fundamental principle of the continuum into the discrete system at a modest computational cost. The construction of such scheme, the main numerical algorithms and their parallelisation on modern supercomputing facilities will be discussed. Finally, an application to the spectrum of homogeneous two-dimensional turbulence will be illustrated.

For more information, please see: https://num-gssi.github.io/seminar/

The seminar will take place in the Main Lecture Hall, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09

— Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io https://ftudisco.gitlab.io/