Data assimilation for dendritic solidification with melt convection: phase-field lattice Boltzmann study

Abstract

Time-resolved in-situ X-ray tomography and high-performance phase-field simulations are state-of-the-art approaches to clarifying dendrite solidification. However, major issues persist, such as the insufficiency of spatiotemporal resolution in experiments and lack of material properties in simulations. To overcome these issues, in this study, we developed a data assimilation system using an ensemble Kalman filter based on the phase-field lattice Boltzmann method as a simulation model for the dendrite solidification of binary alloys with liquid flow. The validity of the developed system was confirmed through twin experiments to infer the kinematic viscosity in a two-dimensional dendrite growth problem with forced convection.

Long-distance settling simulation of equiaxed dendrite by a moving-frame algorithm: phase-field lattice Boltzmann study with parallel-GPU AMR

“…The developed method is expected to apply to the systematic evaluation of the kinetic behavior of equiaxed dendrites. Furthermore, introducing data assimilation [40,41] into the developed PF-LB simulations will enable highly accurate PF-LB simulations that incorporate the settling experiment data into the PF-LB simulations.…”

Development of a data assimilation system for the investigation of the dendrite solidification process by integrating in situ X-ray imaging and phase-field simulation

“…Forecasting and filtering are alternately performed in data assimilation. In this study, PF simulations of columnar dendrite growth were performed during the directional solidification of a binary alloy as the forecasting process, the details of which are provided in the literature [24][25][26]. The state vector calculated in the forecasting process, x t|t-1 (i) , was updated to xt|t (i) during filtering using the following equation [26,29]:…”

“…To validate the developed data assimilation system, twin experiments were performed to estimate the anisotropic strength of the interfacial energy, ε, and solute diffusion coefficient of the liquid, Dl [24]. ε expresses the orientation dependence of the interfacial energy [30] and is identical to ε4 in previous studies [24][25][26]. The observation data were prepared via the PF simulation of columnar dendrite growth during directional solidification in a thin film of Fe-4 wt% Si.…”

“…Data assimilation, originally developed from meteorology and oceanography, is a promising method for integrating experiments and simulations [19,20]. Recently, data assimilation was applied to PF simulations of grain growth [21,22], dendrite solidification [23][24][25][26], and sintering [27,28]. The introduction of data assimilation to integrate in situ X-ray observations and PF simulations is expected to enable the highly accurate prediction of dendrite growth by overcoming the limitations of both methods.…”