A THREE-DIMENSIONAL FINITE-VOLUME/NEWTON METHOD FOR THERMAL-CAPILLARY PROBLEMS

A three-dimensional nite-volume/Newton method is developed for solving thermal-capillary problems in materials processing. The conductive heat transfer, melt{solid interfaces, the melt{gas free surface, and the shape of grown material are calculated simultaneously. The implementation of interface and free surface boundary conditions, as well as co-ordinate transformation, is described in detail. During the Newton itera- tions, due to the complexity of the problem, the Jacobian matrix is estimated by nite di erences, and the linear equations are solved by the ILU(0) preconditioned GMRES iterative method. Nearly quadratic con- vergence of the scheme is achieved. Sample calculations for oating-zone and Stepanov crystal growth are illustrated.