EUROPEAN CONGRESS AND EXHIBITION ON ADVANCED MATERIALS AND PROCESSES - EUROMAT 2021

A novel adaptive meshless solution procedure is applied for the analysis of the mesh-induced anisotropy in the phase-field modelling of dendritic solidification of dilute binary alloys. The adaptive solution procedure is based on the dynamic quadtree domain decomposition which divides the computational domain into quadtree sub-domains of different size. Each quadtree sub-domain has its own distribution of computational nodes in which the meshless radial basis function-generated finite differences (RBF-FD) method and the forward Euler scheme apply for the discretisation of the partial differential equations. The h-adaptivity is ensured by the constant product between the density of computational nodes in a quadtree sub-domain and the area of a quadtree sub-domain. The adaptive time-stepping with different time steps in quadtree sub-domains with different node densities is applied to further speed-up the calculations. The procedure dynamically ensures the highest density of computational nodes at the solid-liquid interface and the lowest density in the bulk of solid and liquid phases. The developed adaptive solution procedure is used to analyse the mesh-induced anisotropy in the solution of the phase-field model for isothermal solidification of a supersaturated dilute binary alloy. The steady-state growth velocities at different preferential growth directions are compared to the reference solution from the literature. The influence of the type of the node distribution (regular or scattered) in a quadtree sub-domain and the size of a local support in the RBF-FD method to the accuracy are analysed. We found out, that the solution is much more prone to the mesh-induced anisotropy effects when the regular node distribution is in use.