A Deterministic Grid-Dependent Bias in Vorticity-Streamfunction Solvers: Observation, Model, and Exact Correction

This is a preprint of the manuscript submitted for peer review. We report a deterministic numerical bias identified in the output stage of vorticity-streamfunction solvers, along with its exact algebraic correction factor. The bias follows the formula (Ny-2)/(Ny-1) for any integer Ny > 2, and is exactly correctable by the factor (Ny-1)/(Ny-2). Three-mesh zero-error prediction and cross-code bit-identical execution confirm the model to machine precision. The accompanying verification software is archived at DOI: 10.5281/zenodo.20607388.