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A finite difference simulation for the bulk single crystal growth of indium phosphide by the liquid encapsulated vertical gradient freezing (LE‐VGF) method with a flat bottom crucible is presented. In order to treat a curvature interface, the boundary fixing method is applied. The transient behavior of the flow and temperature fields, the melt/crystal interface shape and the growth rate during growth are studied numerically. The crystal growth rate is not constant although the temperature lowering rate is constant. The effect of crucible thickness, thermal conductivity of the crucible and temperature of the growth furnace wall on the crystal growth behavior are discussed.