The Cray X1 in the Center for Computational Sciences at Oak Ridge National Laboratory as well as algorithmic improvements over the past decade enable significant new science in the simulation of high-temperature "cuprate" superconductors. We describe the method of dynamic cluster approximation with quantum Monte Carlo, along with its computational requirements. We then show the unique capabilities of the X1 for supporting this method and delivering near optimal performance. This allows us to study systematically the cluster size dependence of the superconductivity in the conventional two-dimensional Hubbard model, which is commonly believed to describe high-temperature superconductors. Due to the non-locality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, converged results are found that display a finite temperature instability to d-wave superconductivity. The results we report here demonstrate for the first time that superconductivity is possible in a system of strongly correlated electrons without the need of a phonon mediated attractive interaction.