A Galerkin projection method for the locally-conservative interpolation of
unstructured grids.

Authors:

Luke J West(1) with Gerard Gorman(2), David Ham(2), Peter Killworth(1), Chris
Pain(2) and Matthew Piggott(2).

(1) National Oceanography Centre, Southampton, UK
(2) Imperial College, London, UK

Abstract:

Interpolating between grids is a common task, and Pointwise Interpolation
(PI) is a common method, but it is not conservative. Therefore, it is
inappropriate for many important diagnostic applications.

For example, in an adaptive framework where regridding occurs frequently, it is
difficult to collect quality temporal statistics using non-conservative methods.

Another example is coupled climate modelling in which surface fluxes between
oceanic and atmospheric components must be conserved even if their respective
surface grids are mutually arbitrary.

To address these and wider problems, a dimension independent algorithm for
generating a supergrid from a set of unstructured grids is developed.

The supergrid embeds each subgrid such that a trivial pointwise interpolation
from any subgrid (onto the supergrid) is not merely conservative but identical,
in the mathematical sense.

The embedding also permits the reverse operation via a Galerkin projection (from
the supergrid) onto any subgrid. This operation is not 'perfect' but guarantees
local (and therefore global) conservation.

Results for a turbulent gravity flow are presented, the accuracy of the method
is analysed, and some wider applications are discussed.