Abstract
Geometric mechanics formulations (GM; variational, Hamiltonian, metriplectic) are a fundamental tool for building physics-based models of many systems, including fluid dynamics. Structure-preserving (SP) discretizations (also known as mimetic or compatible) enable numerical models of GM systems that have discrete analogues of key properties, including conservation laws and involution constraints. This talk will discuss recent progress in discrete exterior calculus (DEC) schemes for fluids, which are a type of staggered finite-volume SP discretization. These advances include higher-order Hodge stars, treatment of arbitrary boundary conditions and structure-preserving, high-order, oscillation-limiting, bounds-preserving (SPHOOL-BP) transport operators.
About the Speaker
Christopher Eldred is a Senior Member of Technical Staff at Sandia National Laboratories in the Computational Mathematics Department. He works on geometric mechanics formulations and structure-preserving discretizations for a variety of physical systems, including both neutral and charged fluid dynamics models. Recently, he has also started working on structure-preserving reduced order modeling and uncertainty quantification.
Host: Professor Theresa Saxton-Fox
