Accuracy of mesh-based cosmological hydrocodes: Tests and corrections

We perform a variety of tests to determine the numerical resolution of the cosmological TVD Eulerian code. Tests include 512(3) and 256(3) simulations of a P-k proportional to k(-1) spectrum to check for self-similarity and a comparison of results with those from higher resolution smooth-particle hy drodynamics (SPH) codes and grid-based calculations. We conclude that in re gions where density gradients are not produced by shocks, the code degrades resolution with a Gaussian smoothing (radius) length of 1.7 cells. At shoc k-caused gradients (for which the code was designed) the smoothing length i s 1.1 cells. Finally, for beta-model-fitted clusters, we can approximately correct the numerical resolution by the transformation R-core(2) --> R-core (2) - (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 s tandard cold dark matter (SCDM) and Lambda CDM models, we find luminosity-w eighted zero-redshift X-ray cluster core radii of 210 +/- 86 h(-1) and 280 +/- 67 h(-1) kpc, respectively, which are marginally consistent with observ ed values of 50-200 h(-1) kpc. Using the corrected core radii, the COBE-nor malized SCDM model predicts a number of bright (L-X > 10(43) ergs s(-1)) cl usters that is too high by a factor of similar to 20, and the Lambda CDM mo del is consistent with observations.