Solar stills represent a promising technology for decentralized freshwater production in arid and semi-arid regions. Nevertheless, their large-scale utilization remains limited by their relatively low distillate productivity and thermal efficiency. To address this limitation, the present study numerically investigates the influence of basin geometry on the thermal performance and productivity of a single-slope solar still. The analysis compares a conventional flat basin with a square-corrugated basin under identical operating conditions, in Basra, Iraq, on 28 October 2025. A transient two-dimensional CFD model was developed in ANSYS Fluent, and the predicted basin-water and glass-cover temperatures were coupled with Dunkle correlations to estimate the hourly and daily distillate yield. The square-corrugated basin showed a clear improvement over the flat basin, with the peak hourly productivity increased from 0.72 to 0.89 kg/m²·h, while the cumulative daily yield increased from 2.97 to 3.9 kg/m²·day. The average daily thermal efficiency also improved from 44.7% to 67.3%. Overall, this geometric modification achieved a 31.12% improvement in freshwater production. These results indicate that increasing the effective heat-transfer area by modifying the basin geometry improved the thermal behavior of the solar still and significantly enhanced its productivity under the same climatic conditions.