Application of a meshless space-time adaptive approach to phase-field modelling of polycrystalline solidification

Abstract We have developed a 2-D numerical meshless adaptive approach for phase-field modelling of dendritic solidification. The quadtree-based decomposes the computational domain into quadtree sub-domains different sizes. algorithm generates uniformly-distributed nodes in each sub-domain. apply radial basis function generated finite difference method and forward Euler scheme to discretise governing equations node. fixed ratio between characteristic size node spacing sub-domain ensures space adaptivity. time-stepping accelerates calculations further. In framework previous research studies, we used solve quantitative models single dendrite growth pure melts dilute binary alloys. present study, upgrade solution procedure multiple differently oriented dendrites. Along with space-time approach, non-linear preconditioning equation increase efficiency. investigate novel approach’s accuracy efficiency by simulating equiaxed from alloy.