A numerical approach for the solution of coupled fluid–solid and thermal stress problems in crystal growth processes

A multigrid finite-volume method for the prediction of thermally coupled fluid–solid problems is applied to crystal growth processes involving heat transfer, thermal stress formation, fluid flow, and mass transfer. For the fluid–solid coupling an unified finite-volume approach, based on the concept of block-structured grids, is employed. A high numerical efficiency is obtained by a global nonlinear multigrid method with a pressure-correction based scheme as smoother. As an exemplary application the scheme is applied to investigate the growth process of silicon carbide bulk crystals. The analysis of a typical growth process shows that temperature inhomogeneities in the growing crystal induce severe thermal stress levels.