Strong-form meshfree collocation method for non-equilibrium solidification of multi-component alloy

This work presents a strong form meshfree collocation method for a multi-phase field model with finite dissipation effects due to rapid solidification. We use the collocation method to simulate and study solidification of a low concentration (0.2 at% Sn) Al–Sn binary alloy system under periodic boundary conditions to address non-equilibrium solidification. Numerical implementation takes place through spatial discretization of the governing equations with the collocation method followed by application of the Crank–Nicolson method to integrate through time. Analysis begins with a benchmark, a simple two-grain case with symmetry in domain size, grain positioning, and boundary conditions to study the behavior of the field equations and key terms embedded within. This occurs by studying field and embedded term values along the axis of symmetry. Solidification analysis is then extended for 10 and 20 grains where upon full solidification, the regions with the highest overall concentrations exist within grain boundary region consisting for four or more adjacent grains. An analysis of alloy solidification over a substrate demonstrates epitaxial nucleation and growth.