Figure 1:
A Cosmological Structure Formation Simulation
An example of a production run using the parallel TVD code.
The gas mesh has a total of 512 cubed (134 million)
points and 256 cubed (17 million) particles represent dark matter.
The computation was done on 64 and 128 nodes of the IBM SP2
at the Cornell Theory Center;
the total running time was four and a half days and
turnaround time was a week.
The simulation volume is a cube with each side 32 megaparsecs in
length (1 parsec = 3.3 light-years).
The pictures below show the projected density of a
slab 8 megaparsec deep taken from the center of the cube; a large cluster
containing X-ray emitting gas forms in the center as gravity
causes dense regions to collapse.
The colors show increasing density in the order black
(least dense), blue, green, yellow, red, white (most dense);
the scale is logarithmic.
90 percent of the mass is in dark matter and the remaining
10 percent is
baryonic (H and He gas); the Hubble constant is 50 km/sec/Mpc
and space is flat.
Figure 1a: Dark matter
The initial dark matter density (redshift z=40).
The simulation begins in the linear regime, when
perturbations from the mean density are small;
thus the density is near average everywhere.
Dark matter density at z=0 (today).
Black regions are empty voids (density is less than a tenth of
the mean density);
white regions are over 250 times denser than the mean.
Thus the particle distribution is highly anisotropic:
many grid points are completely empty and others contain
many thousands of particles.
This movie shows how the dark matter density evolves
in this small patch of the universe.
The overall comsological expansion is shown;
the movie begins when the universe is 1/41 as large as it is today.
Regions of higher density expand slower and regions of low density
expand faster (creating empty voids);
high density regions eventually collapse under
their own gravitational attraction.
Periodic boundary conditions are assumed.
The gas density at z=0 (today).
The original small perturbations are the
same as those for the dark matter shown above.
Temperature of the gas at z=0; black regions are less than
100,000 degrees Kelvin, white regions are over 50 million degrees;
a logarithmic scale is used. It can be seen that the gas
is strongly shocked.
What the gas would appear like in the X-ray today.
The observed properties of X-ray clusters are a useful
means of constraining cosmological theories.
This movie shows how the gas density evolves with time.
This is shown in co-moving coordinates; the overall expansion
of the universe is taken into account as part of the coordinate system.
The wallclock time consumed per step as a function
of the number of processors used. To compare runs with differently
sized grids the times are divided by a factor NX*NY*NZ/128, i.e.
the 256 cubed mesh run times (shown in red) are divided by 8 and the
512 cubed run times (shown in blue) are divided by 64, and so on
(the number of particles is NX*NY*NZ/8 in all cases).
Purple and green represent 768 and 792 cubed meshes.
Circles: total time.
Triangles: purely computational portion of the hydrodynamical code.
Squares:
time required for message passing in solving the TVD equations.
Crosses: the PM portion of the code.
The dashed lines are proportional to 1/NCPU.