Horizontal diffusive flux discretization
The horizontal diffusion for an arbitrary variable (corresponding
to the wind components or the scalar perturbations) is expressed in
flux form in Eq. 92
where the diffusive flux is evaluated using a
forward in space discretization
|
(157) |
and the flux terms for the 1st, 3rd and 5th order differences are
expressed (in one dimension)
from Eq.s 93-94,
respectively, as
where the diffusion coefficients are defined from
Eq.s 101-102.
Note that for
the scalar fluxes, the diffusion coefficients are averaged to the
and points using the same transform as in
Eq.s 128-129.
The odd-ordered
difference schemes are off-centered (upwind), so that the third order
flux is expressed as
|
(161) |
and the 5th order flux is discretized as
|
(162) |
The first order flux uses the same difference scheme as in
Eq. 158.