The phase-field method is an established and versatile tool for the modeling of microstructure evolution in complex systems. We consider the stationary motion of planar interfaces between two phases at different bulk free energy levels. This configuration is used to quantify the influence from artificial grid-friction in different phase-field models. Following the striking ideas from A. Finel et al. [1], we show that restoring translational invariance in a certain direction indeed eliminates artificial grid-friction for interface propagation in this direction. Moreover, the theoretic interface velocities are reproduced by orders of magnitude more accurately, even if the diffuse interface profile is only marginally resolved by just one grid point and less. Finally, we propose a new phase-field model, which restores translational invariance in the direction of local interface motion. We show that, even for marginally resolved interface-profiles, the new model provides frictionless motion for arbitrarily oriented planar interfaces.

Diffuse interface descriptions offer many advantages for the modeling of microstructure evolution. However, the numerical representation of moving diffuse interfaces on discrete numerical grids involves spurious grid friction, which limits the overall performance of the model in many respects. Interestingly, this intricate and detrimental effect can be overcome in finite difference (FD) and fast Fourier transformation (FFT)-based implementations by employing the so-called sharp phase-field method (SPFM). The key idea is to restore the discretization-induced broken translational invariance (TI) in the discrete phase-field equation by using analytic properties of the equilibrium interface profile. We prove that this method can indeed eliminate spurious grid friction in the three-dimensional space. Focusing on homogeneous driving forces, we quantitatively evaluate the impact of spurious grid friction on the overall operational performance of different phase-field models. We show that the SPFM provides superior degrees of interface isotropy with respect to energy and kinetics. The latter property enables the frictionless motion of arbitrarily oriented diffuse interfaces on a fixed 3D grid.

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