Accurate simulation of the anisotropic dendrite crystal growth by the 3DVar data assimilation

Abstract

The growth phenomenon of dendritic crystals is a common occurrence in nature, forming a structure similar to tree branches during its evolution. However, in practical computations, model parameters and initial conditions may have observational errors, which cause large errors in numerical simulation results. To improve the accuracy and efficiency of numerical simulation, this study uses a three-dimensional variational (3DVar) data assimilation algorithm. We consider using the phase-field dendritic crystal growth (PF-DCG) model as the governing equation for numerical simulation. Through the optimization problem of 3DVar, we will incorporate the observed solutions from experimental data into the process of solving numerical solutions to modify them, thereby achieving the goal of data assimilation. This study mainly evaluates two different categories of problems: initial observational errors and model parameter errors. In the numerical experiment section, we obtain the numerical solution by using the operator splitting method (OSM) and explore the effectiveness of this method and investigate the influence of various factors such as adjustment factors, spatio-temporal sampling rates, and parameter perturbation ratios on the effectiveness of data assimilation. The experimental results show that this method can effectively assimilate the observation data, thus accurately simulating the growth process of dendritic crystals.