A fully coupled transient 3-dimensional multi-scale model has been developed to predict the evolution of dendritic growth in alloys.The motivation to use such a method is to both reduce computational costs and increase the size of the computational domain.The model consists of a mixture of finite volume and finite difference solvers integrated within a novel multi-scale method that solves the three sets of equations(electromagnetism,heat transfer/solidification and fluid dynamics)on appropriate length and time scales.A locus-based method,allows for mesh ref'mement in regions of interest localised around the interface,to improve accuracy without incurring significant computational overheads.This method has facilitated modelling the evolution of complex 3-dimensional structures on a single processor within a reasonable amount of time.As a demonstration,the model is applied to a super-cooled dendritic solidification problem,in the presence of a constant high magnetic field.
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