Isotropic finite-difference approximations for phase-field simulations of polycrystalline alloy solidification

Phase-field models of microstructural pattern formation during alloy solidification are commonly solved numerically using the finite-difference method, which is ideally suited to carry out computationally efficient simulations on massively parallel computer architectures such as Graphic Processing Units. However, one known drawback this method that discretization differential terms involving spatial derivatives introduces a spurious lattice anisotropy can influence solid-liquid interface dynamics. We find significant for case polycrystalline dendritic solidification, where crystal axes different grains do not generally coincide with reference lattice. In particular, we used implementation quantitative phase-field model binary both operating state dendrite tip and growth orientation strongly affected by anisotropy. To circumvent problem, use methods in real Fourier space derive approximations leading 2D 3D isotropic at order $h^2$ spacing $h$. Importantly, those include divergence anti-trapping current found have critical selection. The discretizations an approximated form facilitates Fourier-space derivation associated operator $O(h^2)$, but also standard current. Finally, present showing implementations dramatically reduce effects.