Turbulent thermal buoyancy driven flow of the liquefied gas, LNG and LH₂ (liquefied hydrogen) in the spherical enclosure having a free evaporation surface and uniformly insulated outer wall was analyzed with spherical coordinate system. The k -ε two equation models were used for the turbulent calculation and the finite difference method was applied for the numerical calculation. For the discretized spherical coordinate system the numerical satisfaction of the equation of continuity in the nonconservative form is not ensured due to the geometric change of each cell size and to the finite difference approximation of the first order derived from differential equation. Author introduced the equalized flow for the convection terms of equations of enegy, vorticity, turbulent kinetic energy and dissipation rate. The automatic satisfaction of flow continuity over the entire range of control volumes and the stable numerical solutions were obtained by application of this new method. As for the boundary conditions for free surface liquid two kinds of thermal configurations were considered, one of which was heat flux corresponding to an evaporation equivalent to the heat input and the other was saturated temperature corresponding to the vapor pressure. Consequently author evaluated briefly the relations between boil off quantity and fluid flow characterized by the tank shape of spherical and square.