Phase-field models for moving boundary problems: Controlling metastability and anisotropy

We introduce a variant of a recently proposed method of rotated lattices for numerical treatment of moving boundary problems. The usual lattice introduced for numerical computation of phase-field models gives rise to unphysical metastable states and anisotropy. In the present case we rotate and shift the lattice by random angles and fractions of a lattice constant. We show that a twelve point interpolation formula is adequate to keep numerical interpolation errors sufficiently localized. This removes the unphysical metastabilities and makes the model fully isotropic. This is demonstrated by a few example-calculations for dendritic pattern formation.