  We use our new population synthesis code BONNFIRES to test how surface
abundances predicted by rotating stellar models depend on the numerical
treatment of rotational mixing, such as spatial resolution, temporal resolution
and computation of mean molecular weight gradients. We find that even with
identical numerical prescriptions for calculating the rotational mixing
coefficients in the diffusion equation, different timesteps lead to a deviation
of the coefficients and hence surface abundances. We find the surface
abundances vary by 10-100% between the model sequences with short timestep of
0.001Myr to model sequences with longer timesteps. Model sequences with
stronger surface nitrogen enrichment also have longer main-sequence lifetimes
because more hydrogen is mixed to the burning cores. The deviations in
main-sequence lifetimes can be as large as 20%. Mathematically speaking, no
numerical scheme can give a perfect solution unless infinitesimally small
timesteps are used. However, we find that the surface abundances eventually
converge within 10% between modelling sequences with sufficiently small
timesteps below 0.1Myr. The efficiency of rotational mixing depends on the
implemented numerical scheme and critically on the computation of the mean
molecular weight gradient. A smoothing function for the mean molecular weight
gradient results in stronger rotational mixing. If the discretization scheme or
the computational recipe for calculating the mean molecular weight gradient is
altered, re-calibration of mixing parameters may be required to fit
observations. If we are to properly understand the fundamental physics of
rotation in stars, it is crucial that we minimize the uncertainty introduced
into stellar evolution models when numerically approximating rotational mixing
processes.

Solar and Stellar Astrophysics