  We present a detailed analysis of numerical discreteness errors in
two-species, gravity-only, cosmological simulations using the density power
spectrum as a diagnostic probe. In a simple setup where both species are
initialized with the same total matter transfer function, biased growth of
power forms on small scales when the solver force resolution is finer than the
mean interparticle separation. The artificial bias is more severe when
individual density and velocity transfer functions are applied. In particular,
significant large-scale offsets in power are measured between simulations with
conventional offset grid initial conditions when compared against converged
high-resolution results where the force resolution scale is matched to the
interparticle separation. These offsets persist even when the cosmology is
chosen so that the two particle species have the same mass, indicating that the
error is sourced from discreteness in the total matter field as opposed to
unequal particle mass. We further investigate two mitigation strategies to
address discreteness errors: the frozen potential method and softened
interspecies short-range forces. The former evolves particles under the
approximately "frozen" total matter potential in linear theory at early times,
while the latter filters cross-species gravitational interactions on small
scales in low density regions. By modeling closer to the continuum limit, both
mitigation strategies demonstrate considerable reductions in large-scale power
spectrum offsets.
