  We present a quantitative benchmark of multiscale models for dendritic growth
simulations. We focus on approaches based on phase-field, dendritic needle
network, and grain envelope dynamics. As a first step, we focus on isothermal
growth of an equiaxed grain in a supersaturated liquid in three dimensions. A
quantitative phase-field formulation for solidification of a dilute binary
alloy is used as the reference benchmark. We study the effect of numerical and
modeling parameters in both needle-based and envelope-based approaches, in
terms of their capacity to quantitatively reproduce phase-field reference
results. In light of this benchmark, we discuss the capabilities and
limitations of each approach in quantitatively and efficiently predicting
transient and steady states of dendritic growth. We identify parameters that
yield a good compromise between accuracy and computational efficiency in both
needle-based and envelope-based models. We expect that these results will guide
further developments and utilization of these models, and ultimately pave the
way to a quantitative bridging of the dendrite tip scale with that of entire
experiments and solidification processes.
