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The basic discretization, centered second order, is the default. It is
designed to be consistent with the continuity equation to facilitate
conservation properties analogous to the continuum. However, centered
second order advection is notoriously noisy and must be used in
conjunction with some finite amount of diffusion to produce a sensible
solution.
The advection operator is discretized:

(2.171) 
where the area integrated fluxes are given by:
The quantities
,
and
are volume fluxes defined:
For nondivergent flow, this discretization can be shown to conserve
the tracer both locally and globally and to globally conserve tracer
variance,
. The proof is given in Adcroft et al. [1997]; Adcroft [1995].
Next: 2.17.2 Third order upwind
Up: 2.17 Linear advection schemes
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