Data assimilation for three-dimensional phase-field simulation of dendritic solidification using the local ensemble transform Kalman filter

Abstract

Data assimilation (DA) based on Bayes' theorem helps improve the accuracy of numerical models and simultaneously enables the estimation of unknown parameters used in the numerical model by combining simulation results with observational data. We applied the local ensemble transform Kalman filter (LETKF), a computationally efficient and accurate DA methodology, to a phase-field model of dendritic solidification in a binary alloy. We demonstrated the efficiency of LETKF through numerical experiments (twin experiments) wherein we estimated the unknown state of the solidification and the model parameters from synthetic observation datasets of a growing dendrite morphology. Results of the twin experiments show that using LETKF we could successfully estimate three-dimensional (3D) time evolution of the solute concentration-field in the liquid phase. Further, we could inversely identify multiple model parameters, including interfacial energy between the solid and liquid phases and the solute diffusion coefficient in the liquid phase only from the 3D morphological information of a growing dendrite. We demonstrated that the LETKF-based DA method is a promising methodology for performing accurate phase-field simulations in conjunction with experimental data.