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.

[1]  B. Stinner,et al.  Multicomponent alloy solidification: phase-field modeling and simulations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  B. Nestler,et al.  Small strain elasto-plastic multiphase-field model , 2015 .

[3]  William J. Dally,et al.  Technology-Driven, Highly-Scalable Dragonfly Topology , 2008, 2008 International Symposium on Computer Architecture.

[4]  New Metallographic Method for Estimation of Ordering and Lattice Parameter in Ternary Eutectic Systems , 2013, Metallography, Microstructure, and Analysis.

[6]  Ulrich Rüde,et al.  Lehrstuhl Für Informatik 10 (systemsimulation) Walberla: Hpc Software Design for Computational Engineering Simulations Walberla: Hpc Software Design for Computational Engineering Simulations , 2010 .

[7]  T. Takaki,et al.  Unexpected selection of growing dendrites by very-large-scale phase-field simulation , 2013 .

[8]  Alexander Vondrous,et al.  Parallel computing for phase-field models , 2014, Int. J. High Perform. Comput. Appl..

[9]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.

[10]  A. Scotch,et al.  Determination of the eutectic structure in the Ag-Cu-Sn system , 2002 .

[11]  Britta Nestler,et al.  Diffuse interface method for fluid flow and heat transfer in cellular solids , 2014, Adv. Eng. Softw..

[12]  Ibm Redbooks,et al.  IBM System Blue Gene Solution: Blue Gene/P Application Development , 2009 .

[13]  Alexander Vondrous,et al.  Phase‐Field Modeling of Diffusion Coupled Crack Propagation Processes , 2014 .

[14]  S. Fries,et al.  The Ag–Al–Cu system: Part I: Reassessment of the constituent binaries on the basis of new experimental data , 2004 .

[15]  Abhik Choudhury,et al.  Quantitative phase-field model for phase transformations in multi-component alloys , 2013 .

[16]  J. Rutter,et al.  Origin of microstructure in the 332 K eutectic of the Bi-In-Sn system , 1997 .

[17]  S. Fries,et al.  The Ag–Al–Cu system: II. A thermodynamic evaluation of the ternary system , 2005 .

[18]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[19]  N. Moelans A quantitative and thermodynamically consistent phase-field interpolation function for multi-phase systems , 2011 .

[20]  Jin Yu,et al.  Controlling Ag3Sn plate formation in near-ternary-eutectic Sn-Ag-Cu solder by minor Zn alloying , 2004 .

[21]  T. Takaki,et al.  Two-dimensional phase-field simulations of dendrite competitive growth during the directional solidification of a binary alloy bicrystal , 2014 .

[22]  Lorenz Ratke,et al.  Microstructures of Directionally Solidified Al–Ag–Cu Ternary Eutectics , 2012, Transactions of the Indian Institute of Metals.

[23]  B. Nestler,et al.  A method for coupling the phase-field model based on a grand-potential formalism to thermodynamic databases , 2015 .

[24]  Gerhard Wellein,et al.  LIKWID: Lightweight Performance Tools , 2011, CHPC.

[25]  Ulrich Rüde,et al.  Large scale phase-field simulations of directional ternary eutectic solidification , 2015 .

[26]  Gerhard Wellein,et al.  LIKWID: A Lightweight Performance-Oriented Tool Suite for x86 Multicore Environments , 2010, 2010 39th International Conference on Parallel Processing Workshops.

[27]  Amber Genau,et al.  Morphological characterization of the Al–Ag–Cu ternary eutectic , 2012 .

[28]  Ulrich Rüde,et al.  A framework for hybrid parallel flow simulations with a trillion cells in complex geometries , 2013, 2013 SC - International Conference for High Performance Computing, Networking, Storage and Analysis (SC).

[29]  Thomas Böhlke,et al.  Phase-field elasticity model based on mechanical jump conditions , 2015 .

[30]  Satoshi Matsuoka,et al.  Peta-scale phase-field simulation for dendritic solidification on the TSUBAME 2.0 supercomputer , 2011, 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC).

[31]  T. Takaki,et al.  GPU-accelerated phase-field simulation of dendritic solidification in a binary alloy , 2011 .

[32]  Samuel Williams,et al.  Roofline: an insightful visual performance model for multicore architectures , 2009, CACM.

[33]  B. Nestler,et al.  Theoretical and numerical study of lamellar eutectic three-phase growth in ternary alloys. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.