Large-scale parallel lattice Boltzmann–cellular automaton model of two-dimensional dendritic growth

Abstract

An extremely scalable lattice Boltzmann (LB)–cellular automaton (CA) model for simulations of two-dimensional (2D) dendritic solidification under forced convection is presented. The model incorporates effects of phase change, solute diffusion, melt convection, and heat transport. The LB model represents the diffusion, convection, and heat transfer phenomena. The dendrite growth is driven by a difference between actual and equilibrium liquid composition at the solid–liquid interface. The CA technique is deployed to track the new interface cells. The computer program was parallelized using the Message Passing Interface (MPI) technique. Parallel scaling of the algorithm was studied and major scalability bottlenecks were identified. Efficiency loss attributable to the high memory bandwidth requirement of the algorithm was observed when using multiple cores per processor. Parallel writing of the output variables of interest was implemented in the binary Hierarchical Data Format 5 (HDF5) to improve the output performance, and to simplify visualization. Calculations were carried out in single precision arithmetic without significant loss in accuracy, resulting in 50% reduction of memory and computational time requirements. The presented solidification model shows a very good scalability up to centimeter size domains, including more than ten million of dendrites. Program summaryProgram title: 2DdendCatalogue identifier: AEQZ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQZ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, UKLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 29,767No. of bytes in distributed program, including test data, etc.: 3131,367Distribution format: tar.gzProgramming language: Fortran 90.Computer: Linux PC and clusters.Operating system: Linux.Has the code been vectorized or parallelized?: Yes. Program is parallelized using MPI. Number of processors used: 1–50,000RAM: Memory requirements depend on the grid sizeClassification: 6.5, 7.7.External routines: MPI (http://www.mcs.anl.gov/research/projects/mpi/), HDF5 (http://www.hdfgroup.org/HDF5/)Nature of problem:Dendritic growth in undercooled Al–3 wt% Cu alloy melt under forced convection.Solution method:The lattice Boltzmann model solves the diffusion, convection, and heat transfer phenomena. The cellular automaton technique is deployed to track the solid/liquid interface.Restrictions:Heat transfer is calculated uncoupled from the fluid flow. Thermal diffusivity is constant.Unusual features:Novel technique, utilizing periodic duplication of a pre-grown “incubation” domain, is applied for the scaleup test.Running time:Running time varies from minutes to days depending on the domain size and number of computational cores.