Tracer
Advection Code: Second-Order Moments (SOM, 1986)
The
Second-Order Moments advection algorithm has been recoded extensively
since the original 1986 publication.
What is given here along with 1-D and 3-D sample tests is a major
rewrite in vector / intrinsic mode plus two greatly improved flux
limters (see below).
The new INTRINSIC / VECTOR formulation of CTM advection core contains
no conditionals, its abstract coding is correct and easier to follow,
BUT it runs much more slowly than the same code with do-loops on
typical computers (e.g., IBM p-series 8- and 32-proc boards).
Thus you may want to put the do loops and indices back in (as we have
done). Also the allocation of memory every time QVECT is called
also slows down the code. Fixed allocations are what we run with
now.
The flux limiters now include:
LIMTR=0 no limits, neg. tracer allowed
LIMTR=1 pos. definite SOM fix (per
Prather 1986): adjusts QXT & QXX
LIMTR=2 pos. definite & monotonic
(ca. 1994-95): adjust QXT,QXX,QXY,QXZ
LIMTR=3 min/max limiters (revised
2003-2007)
More recently the SOM code-on-a-sphere has improved accuracy and
efficiency:
(1) the vector form, along with the stacking of vertical advection has
increased the efficiency of vertical transport on vector machines:
(2) E-W and N-S flow are now done as continuous loops with
over-the-pole flow treated much more accurately (retaining SOM info).
Sample
tests coded here run test cases in 1-D and 3-D (but not spherical)
through all the
LIMTR options showing how rms error increases slowly but ripples
disppear. A
sample code for the new spherical 3D flow (see PDF figures on the web
site) is being prepared for posting.
Michael Prather
23 Mar 2007
SOM
vector code - standalone 3D (not sphere) with tests (3/2007)
in a zip-file: SOM_2007.zip
Test runs are
included:
compile: SOM3DX.f + QVECT.f (or SOM1DX.f +
QVECT.f)
run as: SOM3DX <stdin.som >
SOM3DX.out
and look at fort.16 (included as SOM3DX.16)
for more details, e.g., tracer patterns.
SOM original paper
M.J. Prather,
Numerical
Advection by Conservation of Second-Order Moments, J. Geophys. Res., 91, 6671-6681,
1986. (Copyright
1986 American Geophysical Union. Further reproduction or electronic
distribution is
not permitted.)
SOM Vectorized Pipe Flow on a
Sphere - schematics
UCIrvine
Chemistry-Transport Model: Tracer Advection with Second-Order Moments
on a Spherical Grid
(OpenMP,
vectorized version 5.0, Apr 2003).
