We systematically explore zero impact parameter collisions of white dwarfs (WDs) with the Eulerian adaptive grid code FLASH for 0.64 + 0.64 M ⊙ and 0.81 + 0.81 M ⊙ mass pairings. Our models span a range of effective linear spatial resolutions from 5.2 × 107 to 1.2 × 107 cm. However, even the highest resolution models do not quite achieve strict numerical convergence, due to the challenge of properly resolving small-scale burning and energy transport. The lack of strict numerical convergence from these idealized configurations suggests that quantitative predictions of the ejected elemental abundances that are generated by binary WD collision and merger simulations should be viewed with caution. Nevertheless, the convergence trends do allow some patterns to be discerned. We find that the 0.64 + 0.64 M ⊙ head-on collision model produces 0.32 M ⊙ of 56Ni and 0.38 M ⊙ of 28Si, while the 0.81 + 0.81 M ⊙ head-on collision model produces 0.39 M ⊙ of 56Ni and 0.55 M ⊙ of 28Si at the highest spatial resolutions. Both mass pairings produce ~0.2 M ⊙ of unburned 12C+16O. We also find the 0.64 + 0.64 M ⊙ head-on collision begins carbon burning in the central region of the stalled shock between the two WDs, while the more energetic 0.81 + 0.81 M ⊙ head-on collision raises the initial post-shock temperature enough to burn the entire stalled shock region to nuclear statistical equilibrium.