  Plasmoid-mediated reconnection plays a fundamental role in different solar
atmospheric phenomena. Numerical reproduction of this process is therefore
essential for developing robust solar models. Our goal is to assess
plasmoid-mediated reconnection across various numerical resistivity models in
order to investigate how plasmoid numbers and reconnection rates depend on the
Lundquist number. We used the Bifrost code to drive magnetic reconnection in a
2D coronal fan-spine topology, carrying out a parametric study of several
experiments with different numerical resolution and resistivity models. We
employed three anomalous resistivity models: (1) the original hyper-diffusion
from Bifrost, (2) a resistivity proportional to current density, and (3) a
resistivity quadratically proportional to electron drift velocity. For
comparisons, experiments with uniform resistivity were also run.
Plasmoid-mediated reconnection is obtained in most of the experiments. With
uniform resistivity, increasing the resolution reveals higher plasmoid
frequency with weaker scaling to the Lundquist number, obtaining 7.9-12
plasmoids per minute for $S_L\in[1.8 \times 10^4, 2.6\times 10^5]$ with a
scaling of $S_L^{0.210}$ in the highest-resolution resistivity cases,
transcending into Petschek reconnection in the high-$S_L$ limit and
Sweet-Parker reconnection in the low-$S_L$ limit. Anomalous resistivity leads
to similar results even with lower resolution. The drift-velocity-dependent
resistivity excellently reproduces Petschek reconnection for any Lundquist
number, and similar results are seen with resistivity proportional to
current-density. Among the different resistivity models applied on the given
numerical resolution, the hyper-diffusion model reproduced plasmoid
characteristics in closest resemblance to those obtained with uniform
resistivity at a significantly higher resolution.
