Geometric mechanics provides a powerful theoretical framework for formulating models in geophysical fluid dynamics. The discretisation of such models poses significant computational challenges, both in representing discretely the structure of the original problem and the corresponding computational cost. In this work we will present recent developments in geometric integration for fluid dynamics in two dimensions. In particular, we will illustrate a recently developed efficient and scalable Lie-Poisson integrator for flows on the sphere. We will show that it is possible to design geometric integrators which conserve the Casimirs of the system at modest computational costs. The construction of such schemes, the main numerical algorithms and their parallelisation on modern supercomputing facilities will be discussed. An application to the spectrum of homogeneous two-dimensional turbulence and quasi-geostrophic turbulence will be illustrated.”
Period
28 Feb 2023
Event title
SIAM Conference on Computational Science and Engineering, CSE 2023