A DNS of the turbulent flow and heat transfer in an idealized Czochralski configuration was conducted using a very fine grid. The results show the irregular forming of buoyant thermal plumes as well as the occurrence of a large, stable vortical structure in the bulk of the melt. In the averaged flow field a Bénard-cell-like pattern can be recognized. The DNS data served also as a reference for the validation of the LES method. The LES computations were conducted using different grid sizes, SGS models, and discretization methods. For relatively fine grids and central differences, the results agree very well with the DNS. Using an upwind discretization introduces numerical errors. In combination with coarser grids, this leads to large deviations and even qualitative differences. However, overall the computational effort could be reduced significantly by LES. Thus a compromise between accuracy achieved and effort required has to be found.