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. Tests include 5123 and 2563 simulations of a Pk∝k−1 spectrum to check for self-similarity and a comparison of results with those from higher resolution smooth-particle hydrodynamics (SPH) codes and grid-based calculations. 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 β-model-fitted clusters, we can approximately correct the numerical resolution by the transformation R2core→R2core-(CΔl)2, where Δl is the cell size and C=1.1-1.7. When we use these corrections on our previously published computations for the standard cold dark matter (SCDM) and ΛCDM models, we find luminosity-weighted zero-redshift X-ray cluster core radii of 210 ± 86 h−1 and 280 ± 67 h−1 kpc, respectively, which are marginally consistent with observed values of 50-200 h−1 kpc. Using the corrected core radii, the COBE-normalized SCDM model predicts a number of bright (LX>1043 ergs s-1) clusters that is too high by a factor of ~20, and the ΛCDM model is consistent with observations.
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