A 2-D finite element model is presented for the melt growth of single crystals in a microgravity environment with a superimposed DC magnetic field. The model is developed using deforming finite element methodology and predicts steady and transient convective flows, heat transfer, solute distribution, and solidification interface morphology associated with the melt growth of single crystals in microgravity with and without an applied magnetic field. Numerical simulations were carried out for a wide range of parameters including idealized microgravity condition, synthesized g-jitter and real g-jitter data taken by on-board accelerometers during space flights. The results reveal that the time varying g-jitter disturbances, although small in magnitude, cause an appreciable convective flow in the liquid pool, which in turn produces detrimental effects during the space processing of single crystal growth. An applied magnetic field of appropriate strength, superimposed on the microgravity, can be very effective in suppressing the deleterious effects resulting from g-jitter disturbances.