An original numerical technique is used to very efficiently simulate the global heat transfer and 3D melt flow in the Czochralski growth of large silicon crystals under the effect of a transverse magnetic field. Several problems are solved including the simulation of an industrial-size furnace while a comparison is successfully drawn with the literature. The Hartmann and parallel layers located along the crystal and crucible walls are well-captured by our method and show to play a key role in the solution iterative search and to strongly affect the transport of oxygen to the crystal. (C) 2012 Elsevier B.V. All rights reserved.