Previous Abstract | Back to Abstracts Page | Next Abstract
The Piecewise Quartic Method, Continuous Isopycnal Coordinates and Why General Coordinate Models Might Still Be Necessary
Alistair Adcroft, Laurent White, Robert Hallberg
Princeton University and NOAA/GFDL
(Abstract received 05/12/2009 for session X)
ABSTRACT
General coordinate models require very accurate regridding and remapping schemes to avoid the spurious diffusion most often associated with Eulerian models. The piecewise quartic method (PQM) is a natural extension of the piecewise parabolic method (PPM) and is shown to be significantly more accurate. Vertical advection in Eulerian models can be interpreted as reconstruction and remapping of the water column and high-order methods naturally lead to improvements in accuracy and fidelity. However, use of high-order reconstructions is at odds with the usual isopycnal interpretation which is piecewise constant by layer. Even though layer models use a low order representation they are the most adiabatic formulation available. With the intent of finding an accurate, adiabatic general coordinate formulation we adopt a continuous isopycnal representation which defines isopycnal coordinates by interface rather than layer. Relaxing the piecewise constant by layer representation impacts many terms in the model, particularly the pressure gradient. A comparison between traditional isopycnal, continuous isopycnal and two Eulerian coordinates validates the approach and provides convincing evidence that Eulerian models still exhibit excessive spurious diffusion even when employing very high-order methods.
Previous Abstract | Back to Abstracts Page | Next Abstract
2009 LOM Workshop, Miami, Florida Jume 1 - 3, 2009