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A scientific benchmark test is carried out for a multi-phase-field model with double-obstacle potential by performing three-dimensional simulations of dendritic growth under directional solidification. The effects of key numerical parameters of the multi-phase-field model such as numerical resolution and interface width on the dendrite tip operating state are studied, optimal parameter values are set, and where the operating state becomes independent of varying these parameters is elaborated. Some uncertainties in the proper choice of effective interface mobility in the thin-interface limit are discussed and a pragmatic solution is adopted. The binary alloy Al-Cu with 4 at.% Cu is chosen as the material system because it has been used in many previous experimental and numerical studies to investigate dendrite morphology under directional solidification. The recently developed sharp phase-field model by Finel and colleagues is adapted to the double-obstacle potential function and included in the benchmark test. It is shown how the sharp phase-field model helps in achieving agreeable convergence with larger discretization, thereby reducing the computational cost significantly. The benchmarks are performed using the OpenPhase software.