novel solution procedure is developed for the phase field-based simulation of dendritic solidification in Fe-C steel. The adaptive solution procedure is based on the dynamic quadtree domain ...decomposition, which divides the computational domain into quadtree sub-domains of different sizes. Each quadtree sub- domain contains a distribution of computational nodes. The meshless radial basis function-generated finite differences method and the forward Euler scheme are applied to discretise the partial differential equations. The h-adaptivity is ensured by keeping a constant number of the nodes in each of the quadtree sub-domains. Different, mutually coordinated stable time steps are used in different quadtree sub-domains. The procedure dynamically ensures the highest density of the computational nodes at the solid-liquid interface and the lowest density in the bulk of the phases. The phase field model, capable of simulating isothermal and non-isothermal solidification of binary alloys, is implemented by the developed adaptive solution procedure. The solution procedure is verified by solving the benchmark for isothermal solidification of binary alloys first. The solution procedure is then used to investigate the constrained growth of a single equiaxed dendrite in carbon steel with imposed cooling rate. The impact of the cooling rate on the dendrite morphology and micro-segregation is analysed. The developments represent a part of the micro- segregation module in multi-scale and multi-physics simulation systems for continuous steel casting.
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