Numerical modeling is applied to investigate the factors affecting the shape of the crystal-melt interface during the growth of Ti-doped sapphire crystals by using the Kyropoulos method. Numerical results are compared to experimental visualization of the growth interface in the case of ingots grown in crucibles of 15 cm in diameter. The transient computations of the heat transfer and melt convection show that the interface curvature depends on the internal radiative effect in the sapphire crystal. The effective thermal conductivity increases significantly in the case of Ti-doped crystals, leading to conical shapes of the interface with large curvatures. The growth interface is less curved in the case of non-doped sapphire crystals which have a smaller absorption coefficient. The convection driven by buoyancy and Marangoni effects has also a strong effect on the interface shape. The intensity of the Marangoni flow increases significantly during the shouldering stage of the growth, leading to a more curved interface with a convex-concave shape. The comparison between numerically computed interface deflection and the experimental results shows a good agreement. According to present numerical analysis, the formation of a plateau and the temporal concave shape of the crystal are related to unfavorable thermal conditions at the beginning of the growth process. (C) 2016 Elsevier B.V. All rights reserved.