High–Performance Computing: Numerical Simulation of the Melt Flow in an Industrial Czochralski Crucible

Abstract

High resolution calculations with about two million control volumes were performed on a parallel-vector computer (NEC SX-4 and SX-5) using a finite volume method and a quasi-DNS approach to simulate the fluid flow and heat transfer in an industrial Czochralski melt. The Czochralski process is the most important production technique for high quality silicon single crystals. The convergence of the numerical algorithm was increased by a factor of 5.3 by utilizing the FAS multigrid method on four grid levels. A time-averaging procedure of the velocities and the temperature results in reduction of the data set which was used to analyze the main transport phenomena in the silicon melt. A total performance of 5.46 and 10.89 GFlops on seven processors was reached for the simulation on the SX-4 and the SX-5, respectively. Based on a comparison of the parallel performance on one to fourteen processors with single- and multigrid, the configuration with fourteen processors gives the highest speedup factor of 9.99 and 8.94, respectively.