  We study a strongly correlated fermionic model with attractive interactions
in the presence of disorder in two spatial dimensions. Our model has been
designed so that it can be solved using the recently discovered meron-cluster
approach. Although the model is unconventional it has the same symmetries of
the Hubbard model. Since the naive algorithm is inefficient, we develop a new
algorithm by combining the meron-cluster technique with the directed-loop
update. This combination allows us to compute the pair susceptibility and the
winding number susceptibility accurately. We find that the s-wave
superconductivity, present in the clean model, does not disappear until the
disorder reaches a temperature dependent critical strength. The critical
behavior as a function of disorder close to the phase transition belongs to the
Berezinsky-Kosterlitz-Thouless universality class as expected. The fermionic
degrees of freedom, although present, do not appear to play an important role
near the phase transition.
