Numerical study of three-dimensional instabilities in a hydrodynamic model of Czochralski growth

A computational approach to the study of three-dimensional instabilities of flows in a Czochralski crucible is proposed. The flow is driven by buoyancy, thermocapillarity and rotation of the crystal and the crucible. The thermal boundary conditions account for the prescribed temperatures or heat flux, as well as convective and radiative heating or cooling of the boundaries. The numerical approach is based on finite volume discretization and consists of a Newton-type solver for the calculation of the steady flow states and an Arnoldi solver for the solution of the eigenvalue problems associated with the linear stability of the flow. Preliminary test calculations and examples of stability studies for the Czochralski melt flow are reported.