Visualization and computational steering of fluid motion in Czochralski crucibles during silicon crystal growth

Abstract

This paper describes the authors' utilization of both post- and co-visualization techniques to indicate details of the fluid motion in a Czochralski crucible. Different visualization methods (particle tracing, isosurface extraction and line integral convolution) are discussed and applied to time-dependent flow in the crucible. Co-visualization is used to investigate the dynamic evolution of the flow structures at high temporal resolution. Moreover, the co-visualization approach also allows for interactive online visualization and computational steering, which strongly increases the user's ability to visualize the results and to supervise and dynamically control the entire computational process. By means of the resulting pictures and animations, the interaction of the different forces, which are responsible for the complex flow in the crucible is illuminated. In this way, the transport processes in the melt flow are characterized. Special attention is paid to the Marangoni-driven convection close to the interface between the melt and the crystal. The methodology for visualization and computational steering described in the paper can be applied to all kinds of complex three-dimensional and unsteady flow simulations. Its application is essential for handling the overwhelming amount of data produced by modern flow predictions. Consequently, it will play a decisive role in the next generation of CFD codes.