The mesoscopic envelope model is a recent multiscale model that is intended to bridge the gap between purely microscopic and macroscopic approaches for the study of dendritic solidification. It consists of the description of a dendritic grain by an envelope that links the active dendrite branches. The envelope growth is deduced from an analytical microscopic model of the dendrite tip growth kinetics matched to the numerical solution of the mesoscopic solute concentration field in the vicinity of the envelope. The branched dendritic structure inside the envelope is described in a volume-averaged sense by phase fractions and averaged solute concentrations. We present a careful quantitative analysis of the influence of numerical and model parameters on the accuracy of the model predictions. We further perform a validation study through comparisons of 3D simulations to experimental scaling laws giving the shape and the internal solid fraction of freely growing binary alloy dendrites and to analytical solutions for the primary dendrite tip speed. We provide generally valid guidelines for the calibration of the mesoscopic model, enabling reliable control of the accuracy of model predictions over a wide range of undercoolings. The model is applied to simulate strong solutal interactions in large ensembles of equiaxed grains. The potential for mesoscopic simulations to provide refined modeling of microstructures in volume-averaged macroscopic models via scale bridging is demonstrated.

We investigate and assess the capability of the mesoscopic envelope model of dendritic solidification to represent the growth of columnar dendritic structures. This is done by quantitative comparisons to phase-field simulations in two dimensions. While the phase-field model resolves the detailed growth morphology at the microscale, the mesoscopic envelope model describes a dendritic grain by its envelope. The envelope growth velocities are calculated by an analytical dendrite-tip model and matched to the numerical solution of the solute concentration field in the vicinity of the envelope. The simplified representation of the dendrites drastically reduces the calculation time compared to phase field. Larger ensembles of grains can therefore be simulated. We show that the mesoscopic envelope model accurately reproduces the evolution of the primary branch structure, the undercooling of the dendrite tips, and the solidification path in the columnar mushy zone. We further show that it can also correctly describe the transient adjustments of primary spacing, both by spacing increase due to elimination of primary branches and by spacing reduction due to tertiary rebranching. Elimination and tertiary rebranching are also critical phenomena for the evolution of grain boundaries between columnar grains that have a different crystallographic orientation with respect to the temperature gradient. We show that the mesoscopic model can reproduce the macroscopic evolution of such grain boundaries for small and moderate misorientation angles, i.e., up to 30 •. It is therefore suitable for predicting the texture of polycrystalline columnar structures. We also provide guidelines for the calibration of the main parameters of the mesoscopic model, required to obtain reliable predictions.