Geodesic
Crystal growth process analysis in case of nonuniform crucible heating
Matematičeskoe modelirovanie, Tome 17 (2005) no. 5, pp. 77-84.

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The thermogravitational convection in melt during crystal growth by Czochralski technique in the case of nonuniform heating of crucible side walls is considered. The numerical simulation is based on the solution of nonstationary three-dimension heat transfer equation and Navier–Stokes equations in Boussinesq approximation. The exponential schemes are used for implementation. 
@article{MM_2005_17_5_a7,
     author = {V. N. Popov and Yu. S. Tsivinskaya and A. E. Kokh},
     title = {Crystal growth process analysis in case of nonuniform crucible heating},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {77--84},
     publisher = {mathdoc},
     volume = {17},
     number = {5},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2005_17_5_a7/}
}
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V. N. Popov; Yu. S. Tsivinskaya; A. E. Kokh. Crystal growth process analysis in case of nonuniform crucible heating. Matematičeskoe modelirovanie, Tome 17 (2005) no. 5, pp. 77-84. http://geodesic.mathdoc.fr/item/MM_2005_17_5_a7/