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This study integrates a large eddy simulation (LES) model and volume of fluid (VOF) method to simulate the free-surface flows over inflexible circular-crested dams of different shapes. The simulated water depths and pressures on the dam surface are validated by the results of laboratory experiments. Then the numerical model examines the effects of the water depths and the Reynolds number on the hydrodynamic force and the discharge coefficient. The simulation results reveal that the time-averaged drag coefficient decreases as the downstream water depth H₂ increases, while the influence of water depth H₂ on the lift coefficients is less significant. Furthermore, the discharge coefficients of circular and elliptical dams, computed from the simulated velocity profiles over the crest of the dam, agree with the formulae suggested by previous studies when the downstream depth H₂/H₁ < 0.90. In contrast, the discharge coefficient of a tear-shape dam is slightly larger than those of circular dams.