Christopher Eldred, Sandia National Laboratory

"Recent Progress in Discrete Exterior Calculus for Fluids"

Abstract: Structure-preserving discretizations such as discrete exterior calculus (DEC) provide a powerful means of constructing numerical models with many desirable properties, including discrete conservation laws, steady geostrophic modes and freedom from spurious computational modes. However, most existing DEC approaches suffer from low order of accuracy, inability to handle arbitrary boundary conditions and low-quality transport operators. In this talk, we will discuss recent work in DEC towards addressing these concerns:
1) consistent treatment of arbitrary boundary conditions on unstructured meshes
2) high-order Hodge star operators on uniform structured meshes
3) structure-preserving, high-order, oscillation limiting (SPHOOL) transport
operators; including optional positivity preservation through uxcorrected transport (FCT).

These advances will be demonstrated in the context of geophysical fluid dynamics, where an operational cloud resolving model (PAM, the Portable Atmospheric Model) based on DEC has been developed.