Experiments have demonstrated biological tissues grow by mechanically sensing their localized curvature, therefore making geometry a key consideration for tissue scaffold design. We developed a simulation approach for modeling tissue growth on beam-based geometries of repeating unit cells, with four lattice topologies considered. In simulations, tissue was seeded on surfaces with new tissue growing in empty voxels with positive curvature. Growth was fastest on topologies with more beams per unit cell when unit cell volume/porosity was fixed, but fastest for topologies with fewer beams per unit cell when beam width/porosity was fixed. Tissue filled proportional to mean positive surface curvature per volume. Faster filling scaffolds had lower permeability, which is important to support nutrient transport, and highlights a need for tuning geometries appropriately for conflicting trade-offs. A balance among trade-offs was found for scaffolds with beam diameters of about 300μm and 50% porosity, therefore providing the opportunity for further optimization based on criteria such as mechanical factors. Overall, these findings provide insight into how curvature-based tissue growth progresses in complex scaffold geometries, and a foundation for developing optimized scaffolds for clinical applications.