  (Abridged) The hot gas in the IGM produces anisotropies in the Cosmic
Microwave Background (CMB) through the thermal Sunyaev-Zel'dovich (SZ) effect.
The SZ effect is a powerful probe of large-scale structure in the universe and
must be carefully subtracted from measurements of the primary CMB anisotropies.
We use moving-mesh hydrodynamical simulations to study the 3-dimensional
statistics of the gas, and compute the mean comptonization parameter and the
angular power spectrum of the SZ fluctuations, for different cosmologies. We
compare these results with predictions using the Press-Schechter formalism. We
find that the two methods agree approximately, but differ in details. We
discuss this discrepancy, and show that resolution limits the reliability of
our results to the 200<l<2000 range. For cluster- normalized CDM models, the SZ
power spectrum is comparable to the primordial power spectrum around l=2000. We
show that groups and filaments (kT<5 keV) contribute about 50% of the SZ power
spectrum at l=500. About half of the SZ power spectrum on these scales is
produced at redshifts z<0.1, and can thus be detected and removed using
existing catalogs of galaxies and X-ray clusters. We discuss the implications
of these results for the future MAP and Planck Surveyor missions.
