Mathematics Seminar - 04/04/24

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. Additionally, I will also discuss structure-preserving time discretizations, specifically a type of discrete gradient scheme that  keeps structure-preserving properties of a spatial discretization.