Large Scale Parallel Lattice Boltzmann Model of Dendritic Growth

"We present a parallel lattice Boltzmann - cellular automaton model of the two-dimensional dendritic growth during solidification of binary alloys. The model incorporates effects of solute and energy transport under melt convection. The parallel performance of the algorithm is assessed. A loss in the parallel efficiency is observed when multiple computational cores per processor are utilized. Excellent strong scaling up to thousands of computing cores is obtained across the nodes of a computer cluster, along with the near-perfect weak scaling up to forty thousand cores. The presented solidification model shows a good scalability up to centimeter size domains, including millions of dendrites.IntroductionLattice Boltzmann method (LBM) is an attractive numerical technique for solving fluid dynamics problems. Its advantages are simple formulation and locality, with locality facilitating parallel implementation. In the present model, interface kinetic is driven by the difference between local actual and local equilibrium liquid composition [1]. The cellular automaton (CA) technique is deployed to track the solid-liquid interface [2]. A serial version of the present LBM-CA model with a small number of dendrites was validated against theoretical and experimental results in the previous publications [3, 4]. In this work, it is the first time that simulations with millions of dendrites were performed, something not possible with the computationally much more costly phasefield method [5].This research effort examines a technique for simulations of millions of dendrites in centimeter size domains, including thermal, convection, and solute redistribution effects. Nearly ideal scaling properties of the model are demonstrated. This extensively large landmark was achieved because of• the CA technique being two orders of magnitude faster than alternative, phase-field methods [5]• highly parallelizable LBM method, convenient for simulations of flow within complex and time dependent boundaries• availability of the powerful NSF Extreme Science and Engineering Discovery Environment (XSEDE) supercomputing resources"