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Phase-field models of microstructural pattern formation during alloysolidification are commonly solved numerically using the finite-differencemethod, which is ideally suited to carry out computationally efficientsimulations on massively parallel computer architectures such as GraphicProcessing Units. However, one known drawback of this method is that thediscretization of differential terms involving spatial derivatives introduces aspurious lattice anisotropy that can influence the solid-liquid interfacedynamics. We find that this influence is significant for the case ofpolycrystalline dendritic solidification, where the crystal axes of differentgrains do not generally coincide with the reference axes of thefinite-difference lattice. In particular, we find that with the commonly usedfinite-difference implementation of the quantitative phase-field model ofbinary alloy solidification, both the operating state of the dendrite tip andthe dendrite growth orientation are strongly affected by the latticeanisotropy. To circumvent this problem, we use known methods in both real andFourier space to derive finite-difference approximations of leadingdifferential terms in 2D and 3D that are isotropic at order $h^2$ of thelattice spacing $h$. Importantly, those terms include the divergence of theanti-trapping current that is found to have a critical influence on patternselection. The 2D and 3D discretizations use an approximated form of theanti-trapping current that facilitates the Fourier-space derivation of theassociated isotropic differential operator at $O(h^2)$, but we also derive a 2Ddiscretization of the standard form of this current. Finally, we present 2D and3D phase-field simulations of alloy solidification, showing that the isotropicfinite-difference implementations can dramatically reduce spurious latticeanisotropy effects.

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