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Description
A novel solution procedure is developed for the phase field-based simulation of dendritic solidification in Fe-C 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 method and the forward Euler scheme are applied for the discretisation of 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 developed adaptive solution procedure is verified by solving the benchmark for isothermal solidification of binary alloys. The solution procedure is demonstrated on the constrained growth of a single equiaxed dendrite in a Fe-C alloy with imposed cooling rate. The impact of the distance between the two neighbouring equiaxed dendrites and the cooling rate to 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 system for continuous casting of steel.