PHASE-FIELD MODELS FOR MOVING BOUNDARY-PROBLEMS - CONTROLLING METASTABILITY AND ANISOTROPY

We introduce a variant of a recently proposed method of rotated lattic es for numerical treatment of moving boundary problems, The usual latt ice introduced for numerical computation of phase-field models gives r ise to unphysical metastable states and anisotropy. In the present cas e 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 localize d. This removes the unphysical metastabilities and makes the model ful ly isotropic. This is demonstrated by a few example-calculations for d endritic pattern formation.