Philipp Steinmetz

Massively parallel phase-field simulations for ternary eutectic directional solidification

Microstructures forming during ternary eutectic directional solidification processes have significant influence on the macroscopic mechanical properties of metal alloys. For a realistic simulation, we use the well established thermodynamically consistent phase-field method and improve it with a new grand potential formulation to couple the concentration evolution. This extension is very compute intensive due to a temperature dependent diffusive concentration. We significantly extend previous simulations that have used simpler phase-field models or were performed on smaller domain sizes. The new method has been implemented within the massively parallel HPC framework waLBerla that is designed to exploit current supercomputers efficiently. We apply various optimization techniques, including buffering techniques, explicit SIMD kernel vectorization, and communication hiding. Simulations utilizing up to 262,144 cores have been run on three different supercomputing architectures and weak scalability results are shown. Additionally, a hierarchical, mesh-based data reduction strategy is developed to keep the I/O problem manageable at scale.

3D Synchrotron Imaging of a Directionally Solidified Ternary Eutectic

For the first time, the microstructure of directionally solidified ternary eutectics is visualized in three dimensions, using a high-resolution technique of X-ray tomography at the ESRF. The microstructure characterization is conducted with a photon energy, allowing to clearly discriminate the three phases Ag2Al, Al2Cu, and α-Aluminum solid solution. The reconstructed images illustrate the three-dimensional arrangement of the phases. The Ag2Al lamellae perform splitting and merging as well as nucleation and disappearing events during directional solidification.

The parallel multi-physics phase-field framework PACE3D

Abstract The phase-field method has been established for the numerical investigation of various microstructure evolution processes. The accurate description of these complex processes requires large domains and suitable models, allowing to couple several physical fields in statistical representative volume elements. To simplify the implementation of new models and to reduce the simulation run time, different frameworks have been developed. In this work, the parallel multi-physics phase-field framework Pace3D is introduced. The general structure of the solver, its modules and the parallelization are described. For increasing the performance of the implemented phase-field models, various optimization techniques are outlined. To efficiently store the simulation results, different data formats and parallel writing mechanisms are presented. The performance of an optimized implementation for a specific phase-field model is analyzed on a single core, showing a good peak performance. For a single node, the memory bandwidth is analyzed and ruled out as possible bottleneck. In addition, a proper weak scaling behavior is demonstrated on the three supercomputers ForHLR I, ForHLR II and Hazel Hen, for up to 96 100 cores.

Quantitative Comparison of Ternary Eutectic Phase-Field Simulations with Analytical 3D Jackson–Hunt Approaches

For the analytical description of the relationship between undercoolings, lamellar spacings and growth velocities during the directional solidification of ternary eutectics in 2D and 3D, different extensions based on the theory of Jackson and Hunt are reported in the literature. Besides analytical approaches, the phase-field method has been established to study the spatially complex microstructure evolution during the solidification of eutectic alloys. The understanding of the fundamental mechanisms controlling the morphology development in multiphase, multicomponent systems is of high interest. For this purpose, a comparison is made between the analytical extensions and three-dimensional phase-field simulations of directional solidification in an ideal ternary eutectic system. Based on the observed accordance in two-dimensional validation cases, the experimentally reported, inherently three-dimensional chain-like pattern is investigated in extensive simulation studies. The results are quantitatively compared with the analytical results reported in the literature, and with a newly derived approach which uses equal undercoolings. A good accordance of the undercooling–spacing characteristics between simulations and the analytical Jackson–Hunt apporaches are found. The results show that the applied phase-field model, which is based on the Grand potential approach, is able to describe the analytically predicted relationship between the undercooling and the lamellar arrangements during the directional solidification of a ternary eutectic system in 3D.

Application of Large-Scale Phase-Field Simulations in the Context of High-Performance Computing

In material science, simulations became a common tool for the understanding of the underlying behaviour of different classes of materials. Due to the growing complexity of problems at hand, the simulation domains, and therefore the computational effort is steadily increasing. We presents various application of the phase-field method; ranging from the solidification of ternary eutectics and pure ice systems to the interaction of multiple liquid phases on fibers. All these topics have in common, that they need a large number of cores to investigate the decisive physical effects in adequate time. We show an overview of the results for this wide range of applications and the scaling behaviour of the used software frameworks.

Large-Scale Phase-Field Simulations of Directional Solidified Ternary Eutectics Using High-Performance Computing

The combination of different chemical elements allows to obtain new and improved materials, as required for novel applications. Especially directionally solidified multicomponent eutectic alloys exhibit a wide range of patterns in the microstructure, which are correlated to the mechanical properties. The pattern formation during solidification depends on the chemical elements and the applied process parameters. Large-scale phase-field simulations are used to study the pattern formation of directional solidified ternary eutectics. Three different systems, starting from a model system towards the system Al-Ag-Cu are investigated, using three growth velocities. The three-dimensional simulation results are quantitatively compared and a broad variety of arising patterns for the studied systems is found. The results of the velocity variation follow the predictions from the analytic Jackson-Hunt approach.