The Unified Danish Eulerian Model (UNI-DEM) is an mathematical model
for performing different comprehensive studies related to
damaging effects from high pollution levels in Denmark and Europe.
The model is described with a system of partial differential
equations (PDEs). The number of equations is equal to the
number of chemical species that are studied by the model.
Three chemical schemes (with 35, 56 and 168 chemical species)
are available at present. The model can be run either as 1-layer
model (a 2-D model) or as 10 layer model (a 3-D model).
Three grids can be specified in the horizontal planes:
(i) a coarse
grid
(corresponding to
grid-squares),
(ii) a coarse
grid
(corresponding to
grid-squares),
(iii) a coarse
grid
(corresponding to
grid-squares).
The application of some splitting procedure following by
a discretization of the spatial derivatives leads to
the solution of several systems of ordinary differential
equations (ODEs) at each time-step. The number of equations
in each system of ODEs is equal to the product of the
number of grid-points and the number of chemical species.
if the
horizontal grid is used in the
3-D model with 168 chemical species, then the number
of equations in each system of ODEs is equal to
.
The number of time-steps for a run covering meteorological data
for one year is 213 120 (corresponding to a time-stepsize
of 150 s).
It is clear that such huge computational tasks
can be treated only if (i) fast numerical methods are
selected, (ii) the code is optimized for running on
computers with multi-hierarchical memories (i.e. if the caches
are properly exploited) and (iii) if parallel computers
are efficiently used. The success achieved in the efforts
to satisfy these three conditions and to carry out long-term
computations with UNI-DEM will be reported in this talk.
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Jerzy Wasniewski
2004-01-23