A Spectral Element Method for the Numerical Simulation of Axisymmetric Flow in Czochralski Crystal Growth

In this paper, a spectral element method (SEM) is applied to simulate the axisymmetric flow in Czochralski crystal growth. The coordinate singularity for 1/r at r=0 is avoided by using the Gauss-Radau type quadrature points for the spatial discretization. The SEM solver is validated by its application to the benchmark problems suggested by Wheeler [1]. The stream function is solved by an artificial Poisson equation with the present method. The results show that it agrees well with available data in the literatures.