We present numerical simulations of vapor pressure controlled (VCz) and liquid encapsulated Czochralski (LEC) crystal growth of GaAs under the influence of a traveling magnetic field (TMF) with melt diameters of approximately 6 in and melt heights of approximately 1.8 in. The TMF is generated by an internal heater-magnet module (HMM) inside the pressure chamber in the growth arrangement and has been developed within the project KRIST (MA) over tildeG, see http://www.kristmag.com. For the global simulation, i.e. for the computation in the entire pressure chamber, the software WIAS-HiTNIHS is used. We validate this software by comparing measured and simulated Lorentz forces. Furthermore, we discuss how to account for effects of non-axisymmetric parts of the growth configuration during the axisymmetric computations performed by WIAS-HiTNIHS. Results computed by stationary global simulations are used as input data for transient local simulations of the melt. For the local simulations, we use the code NAVIER to solve the Navier Stokes equations with the Boussinesq approximation together with the energy equation in an axisymmetric setting. Numerical simulations of the melt in an LEC configuration with an HMM are presented, showing that the Lorentz force generated by a TMF induced from the HMM can damp the temperature oscillations in the Taylor cell below the crystal. (C) 2007 Elsevier B.V. All rights reserved.