We apply the general relativistic resistive magnetohydrodynamics code BHAC to perform a 2D study of the formation and evolution of a reconnection layer in between two merging magnetic flux tubes in Minkowski spacetime .
Small-scale effects in the regime of low resistivity most relevant for dilute astrophysical plasmas are resolved with very high accuracy due to the extreme resolutions obtained with adaptive mesh refinement .
Numerical convergence in the highly nonlinear plasmoid-dominated regime is confirmed for a sweep of resolutions .
We employ both uniform resistivity and non-uniform resistivity based on the local , instantaneous current density .
For uniform resistivity we find Sweet-Parker reconnection , from \eta = 10 ^ { -2 } down to \eta = 10 ^ { -4 } , for a reference case of magnetisation \sigma = 3.33 and plasma- \beta = 0.1 .
For uniform resistivity \eta = 5 \times 10 ^ { -5 } the tearing mode is recovered , resulting in the formation of secondary plasmoids .
The plasmoid instability enhances the reconnection rate to v _ { rec } \sim 0.03 c compared to v _ { rec } \sim 0.01 c for \eta = 10 ^ { -4 } .
For non-uniform resistivity with a base level \eta _ { 0 } = 10 ^ { -4 } and an enhanced current-dependent resistivity in the current sheet , we find an increased reconnection rate of v _ { rec } \sim 0.1 c .
The influence of the magnetisation \sigma and the plasma- \beta is analysed for cases with uniform resistivity \eta = 5 \times 10 ^ { -5 } and \eta = 10 ^ { -4 } in a range 0.5 \leq \sigma \leq 10 and 0.01 \leq \beta \leq 1 in regimes that are applicable for black hole accretion disks and jets .
The plasmoid instability is triggered for Lundquist numbers larger than a critical value of S _ { c } \approx 8000 .