In a special seminar at the U-M Department of Climate and Space, Dr. Christopher Eldred from the Sandia National Laboratories will present a lecture on Tuesday, Sept. 13, from 3:30-4:30pm in the CSRB 2424. The title of his lecture is “Geometric mechanics formulations and structure-preserving discretization in geophysical fluid dynamics.”
The presentation will also be available on Zoom: https://umich.zoom.us/j/99625413934
Geometric mechanics formulations (such as variational/Lagrangian, Hamiltonian, metriplectic, GENERIC, etc.) underlie essentially all of the major equations sets used in the modeling of fluid dynamics, for both reversible (entropy-conserving) and irreversible (entropy-generating) dynamics. Utilizing these formulations, structure-preserving (SP) spatial, temporal and spatiotemporal discretizations such as compatible Galerkin methods, symplectic integrators and discrete exterior calculus (DEC) can be developed by emulating the key features of the relevant continuous geometric structure. A SP discretization approach leads to schemes with many useful properties such as freedom for spurious computational modes, consistent energetics and controlled dissipation of enstrophy or thermodynamic entropy. This talk will discuss the use of geometric mechanics formulations and structure-preserving discretizations in geophysical fluid dynamics (GFD), with a focus on compatible Galerkin methods and DEC for atmospheric modelling; and DEC for ocean modelling.