  Recently, secondary island formation due to the tearing instability of the
Sweet-Parker current sheet was identified as a possible mechanism that can lead
to fast reconnection (less sensitive dependence on Lundquist number $S$) both
in numerical simulations using Particle-in-Cell (PIC) method [Daughton et al.
2009], as well as using resistive magnetohydrodynamics (MHD) [Lapenta 2008;
Bhattacharjee et al. 2009]. This instability is thought to appear when $S$ is
greater than a certain threshold. These recent results prompt us to perform
more resistive MHD simulations of a basic reconnection configuration based on
the island coalescence instability, using much higher resolutions and larger
$S$. Our simulations are based on a fairly standard pseudo spectral code, which
has been tested for accuracy, convergence, and compared well with codes using
other methods [Ng et al. 2008]. In our simulations, formation of plasmoids were
not found, except when insufficient resolution was used, or when a small amount
of noise was added externally. The reconnection rate is found to follow the
Sweet-Parker scaling when no noise is added, but increases to a level
independent of $S$ with noise, when plasmoids form. Latest results with $S$ up
to $2 \times 10^5$ will be presented.
