Three-dimensional simulation of flow and thermal field in a Czochralski melt using a block-structured finite-volume method

[1]  K. Kakimoto,et al.  Transient three-dimensional numerical computation for unsteady oxygen concentration in a silicon melt during a Czochralski process under a cusp-shaped magnetic field , 2001 .

[2]  N. Imaishi,et al.  Three-dimensional numerical simulation of spoke pattern in oxide melt , 1999 .

[3]  J. Derby,et al.  On the formation of rotational spoke patterns during the Czochralski growth of bismuth silicon oxide , 1999 .

[4]  Y. Kishida,et al.  Geostrophic turbulence in CZ silicon crucible , 1999 .

[5]  N. Saito,et al.  Pattern transition of temperature distribution at Czochralski silicon melt surface , 1997 .

[6]  Franz Durst,et al.  a Parallel Block-Structured Multigrid Method for the Prediction of Incompressible Flows , 1996 .

[7]  Jeffrey J. Derby,et al.  Three-dimensional melt flows in Czochralski oxide growth: high-resolution, massively parallel, finite element computations , 1995 .

[8]  Masahito Watanabe,et al.  Flow instability of the melt during Czochralski Si crystal growth: dependence on growth conditions; a numerical simulation study , 1994 .

[9]  G. Müller,et al.  Experimental observation and numerical simulation of wave patterns in a Czochralski silicon melt , 1994 .

[10]  Georg Müller,et al.  Modelling of thermal fluid flow in the liquid encapsulated Czochralski process and comparison with experiments , 1994 .

[11]  N. Taniguchi,et al.  Numerical investigation of three-dimensional melt convection with the magnetic Czochralski method , 1994 .

[12]  Brian Cabral,et al.  Imaging vector fields using line integral convolution , 1993, SIGGRAPH.

[13]  G. Müller Convective instabilities in melt growth configurations , 1993 .

[14]  Masahito Watanabe,et al.  Ordered structure in non-axisymmetric flow of silicon melt convection , 1993 .

[15]  K. Hoshikawa,et al.  Three-dimensional numerical analyses of the effects of a cusp magnetic field on the flows, oxygen transport and heat transfer in a Czochralski silicon melt , 1992 .

[16]  Milovan Peric,et al.  Numerical simulation of a 3D Czochralski-melt flow by a finite volume multigrid-algorithm , 1992 .

[17]  J. Lumley,et al.  Instabilities, transition and turbulence in the Czochralski crystal melt , 1992 .

[18]  K. Wingerath,et al.  Instability of the bouyancy driven convection in Si melts during Czochralski crystal growth , 1989 .

[19]  A. Bottaro,et al.  Three-dimensional thermal convection in Czochralski melt , 1989 .

[20]  Adrian D. Jones,et al.  Flow in a model Czochralski oxide melt , 1989 .

[21]  Adrian D. Jones Scaling analysis of the flow of a low Prandtl number Czochralski melt , 1988 .

[22]  M. Mihelčić,et al.  Three-dimensional simulations of the Czochralski bulk flow , 1984 .

[23]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[24]  A. J. Valentino,et al.  The effect of melt flow phenomena on the perfection of czochralski grown gadolinium gallium garnet , 1978 .

[25]  C. Brandle Simulation of fluid flow in Gd3Ga5O12 melts , 1977 .

[26]  Richard L. Pfeffer,et al.  An experimental study of the effects of Prandtl number on thermal convection in a rotating, differentially heated cylindrical annulus of fluid , 1976, Journal of Fluid Mechanics.

[27]  J. Brice,et al.  The Czochralski growth of Bi12SiO20 crystals , 1974 .

[28]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[29]  H. L. Stone ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS , 1968 .

[30]  B. Basu,et al.  Numerical Simulation of Fluid Flow and Heat Transfer in an Industrial Czochralski Melt Using a Parallel-Vector Supercomputer , 2000 .

[31]  Michael Schäfer,et al.  Efficient Simulation of Incompressible Viscous Flows on Parallel Computers , 1996 .

[32]  M. Peric,et al.  Prediction of Three-Dimensional Unsteady Lid-Driven Cavity Flow , 1992 .

[33]  W. E. Langlois Buoyancy-Driven Flows in Crystal-Growth Melts , 1985 .