Институт вычислительной математики
и математической геофизики

The International Conference on Computational Mathematics


Numerical solution of differential and integral equations

Melt convection under conditions of crucible nonuniform lateral walls heating

Popov V.N., Tsivinskaya Yu.S., Kokh A.E., Kokh K.A.

ITAM SD RAS (Novosibirsk),
Institute of Mineralogy and Petrography SD RAS (Novosibirsk)

The mathematical model of fluid convection in cylindrical vessel influenced by stationary nonuniform heating of it`s lateral walls is considered. The numerical simulation based on the joint solution of the three-dimensional heat transfer equation and Navier-Stokes equations in Boissinesq approximation. The algorithm, which can be obtained after transformation of the original not self-adjoined equations to the self-adjoined form is suggested. It implyies that the difference schemes on the uniform spatial grid have the second order of accuracy and the obtained set of difference equations are monotonic independently of time and spatial steps correlation. Results of test problem solution are presented.

The method is applied on the model described by the time-dependent three-dimensional Navier-Stokes equations in Boissinesq approximation. The numerical computations are made and the features of the complex tree-dimensional currents in cylindrical vessel under conditions of lateral walls nonuniform heating are discovered. The opportunity of additional intermixing of the melt with characteristics BSO is shown by the results of the numerical experiments. It leads to reduction of the impurity distribution nonuniformity and promotes the accelerated crystal growth

Note. Abstracts are published in author's edition

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