  Several software packages for relativistic cosmological simulations that do
not fully implement the Einstein equation have recently been developed. Two of
the free-licensed ones are inhomog and gevolution. A key question is whether
globally emergent volume evolution that is faster than that of a Friedmannian
reference model results from the averaged effects of structure formation.
Checking that emergent volume evolution is correctly modelled by the packages
is thus needed. We numerically replace the software's default random
realisation of initial seed fluctuations by a fluctuation of spatially constant
amplitude in a simulation's initial conditions. The average volume evolution of
the perturbed model should follow that of a Friedmannian expansion history that
corresponds to the original Friedmannian reference solution modified by the
insertion of the spatially constant perturbation. We derive the equations that
convert from the perturbed reference solution to the effective solution. We
find that inhomog allows emergent volume evolution correctly at first order
through to the current epoch. For initial conditions with a resolution of $N =
128^3$ particles and an initial non-zero extrinsic curvature invariant $I_i =
0.001$, inhomog matches an exact Friedmannian solution to -0.0058% (Einstein-de
Sitter, EdS) or -0.0033% (LCDM). We find that gevolution models the decaying
mode to fair accuracy, and excludes the growing mode by construction. For $N =
128^3$ and an initial scalar potential $\Phi$ = 0.001, gevolution is accurate
for the decaying mode to 0.012% (EdS) or 0.013% (LCDM). We conclude that this
special case of an exact non-linear solution for a perturbed Friedmannian model
provides a robust calibration for relativistic cosmological simulations.
