The numerical method based on the idea of splitting on physical processes is proposed for investigations of convective motions of fluid in three-dimensional domains with fixed impermeable boundaries. Splitting into two stages (convection transfer and diffusion transfer) is carried out for the convection equations written in physical variables. The stage of convection is realized for velocity components. On the stage of diffusion the new required functions are used: rotor of velocity and vector potential. Such approach gives a possibility to avoid the computation of pressure and to have the solenoidality of the velocity field. Finally a so-called #diffusive# velocity is received as a velocity of fluid.