Modeling of the eutectic system NiAl-34Cr with phase-field simulations based on the Grand potential approach. Two- as well as three-dimensional large-scale phase-field simulations for three different velocities. Comparison of simulation results with analytical theory of Jackson and Hunt in 2D and 3D. The simulations of all considered velocities match well with the analytic approach. Large-scale simulations are found to be in good qualitative and quantitative accordance with experimental results.