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

2012 ◽  
Vol 452-453 ◽  
pp. 1195-1199
Author(s):  
Zhou Hua Qiu ◽  
Zhong Zeng ◽  
Huan Mei ◽  
Li Ping Yao ◽  
Qiu Ming Liu
Keyword(s):  
Numerical Simulation ◽  
Crystal Growth ◽  
Spectral Element Method ◽  
Axisymmetric Flow ◽  
Spectral Element ◽  
Czochralski Crystal Growth ◽  
Element Method

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

2012 ◽  
Vol 452-453 ◽  
pp. 1195-1199
Author(s):  
Zhou Hua Qiu ◽  
Zhong Zeng ◽  
Huan Mei ◽  
Li Ping Yao ◽  
Qiu Ming Liu
Keyword(s):  
Numerical Simulation ◽  
Crystal Growth ◽  
Present Method ◽  
Spectral Element Method ◽  
Axisymmetric Flow ◽  
Spectral Element ◽  
Benchmark Problems ◽  
Czochralski Crystal Growth ◽  
Coordinate Singularity ◽  
Element Method

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.

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