  We perform a variety of tests to determine the numerical resolution of the
cosmological TVD eulerian code developed by Ryu et al (1993). Tests include
512^3 and 256^3 simulations of a Pk=k^{-1} spectrum to check for
self-similarity and comparison of results with those from higher resolution SPH
and grid-based calculations (Frenk et al 1998). We conclude that in regions
where density gradients are not produced by shocks the code degrades resolution
with a Gaussian smoothing (radius) length of 1.7 cells. At shock caused
gradients (for which the code was designed) the smoothing length is 1.1 cells.
Finally, for \beta model fit clusters, we can approximately correct numerical
resolution by the transformation R^2_{core}\to R^2_{core}-(C\Delta l)^2, where
\Delta l is the cell size and C=1.1-1.7. When we use these corrections on our
previously published computations for the SCDM and \Lambda CDM models we find
luminosity weighted, zero redshift, X-ray cluster core radii of (210\pm 86,
280\pm 67)h^{-1}kpc, respectively, which are marginally consistent with
observed (Jones & Forman 1992) values of 50-200h^{-1}kpc. Using the corrected
core radii, the COBE normalized SCDM model predicts the number of bright
L_x>10^{43}erg/s clusters too high by a factor of \sim 20 and the \Lambda CDM
model is consistent with observations.
