Contactless melt flow control is important in many crystal growth technologies. Typically, steady magnetic fields are used to damp convective flow. On the other hand active flow driving forces like in a rotating magnetic field can be of stabilizing character, too. We present numerical results for the combined action of steady and alternating magnetic fields for the silicon Czochralski crystal growth process. The melt flow is determined by various flow driving sources: besides the thermal convection and rotation of crystal and crucible, there are also the influence of driving and/or damping electromagnetic forces and the thermocapillarity-driven flow at the free deformable melt surface.