  We quantify the error in the results of mixed baryon--dark-matter
hydrodynamic simulations, stemming from outdated approximations for the
generation of initial conditions. The error at redshift 0 in contemporary large
simulations, is of the order of few to ten percent in the power spectra of
baryons and dark matter, and their combined total-matter power spectrum. After
describing how to properly assign initial displacements and peculiar velocities
to multiple species, we review several approximations: (1) {using the
total-matter power spectrum to compute displacements and peculiar velocities of
both fluids}, (2) scaling the linear redshift-zero power spectrum back to the
initial power spectrum using the Newtonian growth factor ignoring homogeneous
radiation, (3) using longitudinal-gauge velocities with synchronous-gauge
densities, and (4) ignoring the phase-difference in the Fourier modes for the
offset baryon grid, relative to the dark-matter grid. Three of these
approximations do not take into account that dark matter and baryons experience
a scale-dependent growth after photon decoupling, which results in directions
of velocity which are not the same as their direction of displacement. We
compare the outcome of hydrodynamic simulations with these four approximations
to our reference simulation, all setup with the same random seed and simulated
using Gadget-III.
