On the rotation invariance of multi-order parameter models for grain growth

In this paper, the rotation invariance of multi-order parameter or multi-phase field models for grain growth in systems with anisotropic properties is verified. The main conclusion is that these models can be considered to be rotationally invariant, if a sufficient number of discrete orientations (namely phase fields or order parameter fields) is used, which is perfectly feasible when sparse data structure algorithms are used for the numerical solution.