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Thermal-electrical-fluid coupled finite element analyses are performed in the model of the growth cell in a high-pressure and high-temperature (HPHT) cubic apparatus in which the large diamond crystal can be grown by using Ni-based solvent with temperature gradient method (TGM). The convection in the Ni-based solvent with different thicknesses at 1700-1800 K is simulated by finite element method (FEM). The experiments of diamond crystal growth are also carried out by using Ni-based solvent at 5.7 GPa and 1700-1800 K in a China-type cubic high pressure apparatus (CHPA). The simulation results show that the Rayleigh number in the solvent is enhanced obviously with the increasing solvent thickness. Good quality diamond single crystal cannot be grown if the Rayleigh number in the solvent is too high.