Title:
The Piece-wise Exponential Method and Its Applications on the Vortex
Decay Problem

Abstract:
Finite volume methods are a major branch of computational fluid
dynamics. A key component of these methods is reconstructing spatially
continuous functions from cell-averaged variables. This proceedure often
struggles between minimizing numerical diffusivity in smooth, continuous
flow, and reducing spurious oscillations near discontinuities. In this
talk, I will introduce a novel reconstruction scheme called the
"piece-wise exponential method (PEM)", which is 3rd order in space and
uses a 3-point stencil. Its complexity is similar to the popular
piece-wise linear method (PLM), but is simultaneously less diffusive in
advection problems and less oscillatory near shocks. In some tests, PEM
even outperforms the piece-wise parabolic method (PPM), which is a
significantly more complex scheme that uses a 5-point stencil. We make
use of PEM and study how thermal cooling affects vortex decay. We
demonstrate that when the cooling time is similar to the vortex turnover
time, the vortex can decay rapidly. This potentially explains the lack
of vortices in protoplanetary disks.