Reduction of discretisation-induced anisotropy in the phase-field modelling of dendritic growth by meshless approach

A numerical procedure is developed to assess and reduce the discretisation-induced anisotropy in the solution of the phase-field model for dendritic growth. The meshless radial basis function-generated finite difference (RBF-FD) method and the forward Euler scheme are used for the spatial and temporal discretisation of the phase-field equations, respectively. A second-order accurate RBF-FD method is ensured by the use of augmentation with monomials up to the second order, while shape-parameter-free polyharmonic splines of the fifth-order are used as the radial basis functions. The performance of the RBF-FD method is assessed on regular and scattered node distributions by observing the mean phase field, the size of the primary dendrite arm, and the growth velocity. The observables at different orientation angles are compared to assess the orientation dependence of the solution. We show for the first time that the use of the RBF-FD method on a scattered node distribution provides a robust approach for the solution of the phase-field model for dendritic solidification with respect to an arbitrary preferential growth direction.