Numerical Analysis and Scientific Computing Seminar | Chris Elder, Geometric mechanics and structure-preserving discretizations for models of physical systems

Geometric mechanics formulations (variational, Hamiltonian, metriplectic, etc.) provide a powerful description of physical systems, with deep connections to fundamental features such as conservation laws and involution constraints. Structure-preserving numerical discretizations then give a pathway to constructing numerical models of geometric mechanics formulations with the same key properties. This talk will discuss the application of these ideas to fluid dynamics, and illustrate it with examples from electrodynamics and low-Mach (incompressible or semi-compressible) fluid dynamics. Additionally, there will be a short discussion on possible approaches for extending these ideas to systems with discontinuities, such as high-Mach (compressible) fluid dynamics.