Flow direction modeling consists of (1) an accurate representation of the river network and (2) digital elevation model (DEM) processing to preserve characteristics with hydrological significance. In part 1 of our study, we presented a mesh-independent approach to representing river networks on different types of meshes. This follow-up part 2 study presents a novel DEM processing approach for flow direction modeling. This approach consists of (1) a topological relationship-based hybrid breaching-filling method to conduct stream burning for the river network and (2) a modified depression removal method for rivers and hillslopes. Our methods minimize modifications to surface elevations and provide a robust two-step procedure to remove local depressions in DEM. They are mesh-independent and can be applied to both structured and unstructured meshes. We applied our new methods to the Susquehanna River Basin with different model configurations. The results show that topological relationship-based stream burning and depression-filling methods can reproduce the correct river networks, providing high-quality flow direction and other characteristics for hydrologic and Earth system models.