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Recent studies have shown that by utilizing the interactions among median fins (the dorsal, anal, and caudal fins), fishes can achieve higher propulsion performance at the caudal fin. This work aims at a systematic study of the effects of dorsal/anal fin shape and flapping phase on the hydrodynamic performance due to median-fin interactions (MFI) in underwater propulsion using a three-dimensional bluegill sunfish model. Flow simulations were conducted on stationary Cartesian grids using an immersed-boundary-method-based incompressible Navier-Stokes flow solver. The results showed that, due to the collision between the posterior body vortices (PBVs) and caudal fin leading edge vortices (LEVs), the latter is strengthened. As a result, the thrust and efficiency of the caudal fin are improved simultaneously, by 25.6% and 29.2%, respectively. Increases in the dorsal/anal fin area result in stronger caudal fin LEVs …