Search

Abstract In the engineering field, it is necessary to construct a numerical model that can reproduce multiphase flows containing three or more phases with high accuracy. In our previous study, by extending the conservative Allen–Cahn (CAC) model, which is computationally considerably more efficient than the conventional Cahn–Hilliard (CH) model, to the multiphase flow problem with three or more phases, we developed the conservative Allen–Cahn type multi-phase-field (CAC–MPF) model. In this study, we newly construct the improved CAC–MPF model by modifying the Lagrange multiplier term of the previous CAC–MPF model to a conservative form. The accuracy of the improved CAC–MPF model is evaluated through a comparison of five models: three CAC–MPF models and two CH–MPF models. The results indicate that the improved CAC–MPF model can accurately and efficiently perform simulations of multiphase flows with three or more phases while maintaining the same level of volume conservation as the CH model. We expect that the improved CAC–MPF model will be applied to various engineering problems with multiphase flows with high accuracy. Graphic abstract

In the phase-field simulation of dendrite growth during the solidification of an alloy, the computational cost becomes extremely high when the diffusion length is significantly larger than the curvature radius of a dendrite tip. In such cases, the adaptive mesh refinement (AMR) method is effective for improving the computational performance. In this study, we perform a three-dimensional dendrite growth phase-field simulation in which AMR is implemented via parallel computing using multiple graphics processing units (GPUs), which provide high parallel computation performance. In the parallel GPU computation, we apply dynamic load balancing to parallel computing to equalize the computational cost per GPU. The accuracy of an AMR refinement condition is confirmed through the single-GPU computations of columnar dendrite growth during the directional solidification of a binary alloy. Next, we evaluate the efficiency of dynamic load balancing by performing multiple-GPU parallel computations for three different directional solidification simulations using a moving frame algorithm. Finally, weak scaling tests are performed to confirm the parallel efficiency of the developed code.

The present study proposes multi-scale topology optimization for polycrystalline microstructures applying a multi-phase field method. The objective function is to maximize the heat compliance of macrostructure and the equality constraint is the material volume of constituents in an alloy consisting of two components with different heat conductivity. Two-scale steady-state heat conduction problem based on a homogenization method is conducted. The Allen-Cahn non-conserved time evolution equation with the additional volume constraint scheme is employed as the optimization strategy for updating the crystal configuration. In the time evolution equation, sensitivities of objective function with respect to phase-field variables are considered to relate topology optimization to the multi-phase field method. It is verified from a series of numerical examples that the proposed method has great potential for the development of material design underlying polycrystalline structure.

Thanks to the recent progress in high-performance computational environments, the range of applications of computational metallurgy is expanding rapidly. In this paper, cutting-edge simulations of solidification from atomic to microstructural levels performed on a graphics processing unit (GPU) architecture are introduced with a brief introduction to advances in computational studies on solidification. In particular, million-atom molecular dynamics simulations captured the spontaneous evolution of anisotropy in a solid nucleus in an undercooled melt and homogeneous nucleation without any inducing factor, which is followed by grain growth. At the microstructural level, the quantitative phase-field model has been gaining importance as a powerful tool for predicting solidification microstructures. In this paper, the convergence behavior of simulation results obtained with this model is discussed, in detail. Such convergence ensures the reliability of results of phase-field simulations. Using the quantitative phase-field model, the competitive growth of dendrite assemblages during the directional solidification of a binary alloy bicrystal at the millimeter scale is examined by performing two- and three-dimensional large-scale simulations by multi-GPU computation on the supercomputer, TSUBAME2.5. This cutting-edge approach using a GPU supercomputer is opening a new phase in computational metallurgy.

A numerical model and computational procedure for static recrystallization are developed using a phase-field method coupled with crystal-plasticity theory. In this model, first, the microstructure and dislocation density during the deformation process of a polycrystalline metal are simulated using a finite element method based on strain-gradient crystal-plasticity theory. Second, the calculated data are mapped onto the regular grids used in the phase-field simulation. The stored energy is calculated from the dislocation density and is smoothed to avoid computational difficulty. Furthermore, the misorientation required for nucleation criteria is calculated at all grid points. Finally, phase-field simulation of the nucleation and growth of recrystallization is performed using the mapped data. By performing a series of numerical simulations based on the proposed numerical procedure, it has been confirmed that the recrystallization microstructure can be reproduced from the deformation microstructure.