A simple Lagrangian travelling slice model has been successfully used to predict the relations between the process parameters and the strand temperatures in the continuous casting of steel. The present paper aims to include a simple macrosegregation, grain structure and mechanical stress and deformation model on top of the thermal slice framework. The basis of all the mentioned models is the slice heat-conduction model that considers the complex heat extraction mechanisms in the mould, with the sprays, rolls, and through radiation. Its main advantage is the fast calculation time, which is suitable for the online control of the caster. The macroscopic thermal and species transfer models are based on the continuum mixture theory. The macrosegregation model is based on the lever rule microsegregation model. The thermal conductivity and species diffusivity of the liquid phase are artificially enhanced to consider the convection of the melt. The grain structure model is based on cellular automata and phase-field concepts. The calculated thermal field is used to estimate the thermal contraction of the solid shell, which, in combination with the metallostatic pressure, drives the elastic-viscoplastic solid-mechanics models. The solution procedure of all the models is based on the meshless radial basis function generated finite difference method on the macroscopic scale and the meshless point automata concept on the grain structure scale. Simulation results point out the areas susceptible to hot tearing.

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