•By GCI evaluation method to study grid independence and discrete error of hydrofoil.•Numerical simulation of the hydrofoil using various turbulence models.•Simulation results consistent with the experiments are obtained through the DCMFBM turbulence model.•Revealing the mechanism of hydrofoil cavities instability and shedding. To improve the accuracy of hydrofoil unsteady cavitation simulations, we investigate grid irrelevance and discrete error using the GCI evaluation method to determine the optimal number of grids. Numerous turbulent viscosity correction approaches are used to improve the turbulence model, and numerical simulations are conducted in conjunction with unsteady cavitation of the hydrofoil with a 3° angle of attack, as well as application evaluation. The results indicate that the DCMFBM model produces the most accurate unsteady cavity shape of the hydrofoil surface. The details of the cavity's primary and secondary shedding are captured during the cavitation process. The DCMFBM turbulence model with a density correction index of 10 and a filter parameter of 0.15c has the highest simulation accuracy. The flow structures of sheet cavitation, transition state cavitation, cloud cavitation, and cavitation shedding are analyzed. The mechanism of hydrofoil cavitation instability and shedding is revealed, providing a theorem. Display omitted