Accuracy of Mesh Based Cosmological Hydrocodes: Tests and Corrections

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Abstract
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.

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