We have developed an efficient and accurate numerical implementation for pore-morphological modeling of drainage in two-dimensional, totally wetting porous media. The new numerical method uses level sets to describe the fluid distribution and polygons that can be defined with subgrid scale accuracy for the pore boundaries, while a previously developed approach represents the phases by pixels arranged on a square lattice. We analyze and compare the previous and new method. For both approaches, the simulated fluid saturations are first-order accurate. For the level-set approach, the simulated interfacial lengths converge to the real values, while the pixel approach yields biased results. The level-set method is orders of magnitudes faster than the pixel method.