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The multi-phase field method is a modem and flexible numerical tool to calculate the structural development during phase transitions. Primarily being developed for solidification problems, it can be effectively applied to solid state transformations driven by diffusion and/or reduction of interfacial area. Curvature effects and topological rearrangement of grain boundary networks are incorporated in a comprehensive way. The paper presents simulations of grain growth scenarios in 2D and 3D isotropic growth and the effect of impurity drag. Impurity drag is described by a simple model, where the "loaded" and "free" part of the grain boundary is distinguished depending on the local velocity of the grain boundary. This treatment allows for the consideration of hysteresis effects. The model is calibrated by comparison with bicrystal experiments taken from the literature.