Diffuse interface descriptions offer many advantages for the modeling of microstructure evolution, where the motion of surface-type defects is driven by volumetric driving forces. The diffuse interface serves as a "smeared out" volumetric surrogate for the surface-type defect.
Numerically under-resolved diffuse interfaces are energetically unstable or subjected to spurious  grid friction, grid anisotropy or the “pinning” on the computational grid. Finel et al. challenged the understanding of the minimal necessary spatial resolution: The sharp phase-field model globally restores Translational Invariance (TI) and operates with one-grid-point interfaces resolutions.
We propose a new sharp phase-field formulation, which locally restores TI in the local interface normal direction.
We evaluate the operational resolution limits of different conventional and sharp phase-field models.
The energetic stability limit of a diffuse interface model is provided by the dimensionless driving force, i.e. the ratio between the driving force volume-density and the interface energy area-density multiplied by the numerical grid spacing.
For the first time, reasonable 3D phase-field operation with a one-grid-point interface resolution at dimensionless driving forces beyond 100 is demonstrated.
Highly efficient simulations of diffusion limited solidification using the newly proposed model provide the expected isotropic seaweed or dense branching microstructures, without any artificial dendritic selection by grid anisotropy.