A numerical method built on an idea of splitting into physical processes is proposed for investigation of the convective fluid flows in the two-dimensional domains with fixed impermeable boundaries. The splitting into physical processes in the problems of hydrodynamics is based on the weak approximation method and on justification of their additivity for the sufficiently small time steps (N.N. Yanenko, 1967; G.I. Marchuk, 1988; A.A. Samarsky, 1965).

The splitting into two steps (the convective and diffusive transfers) is carried out in the convection equations written in the physical variables. The step of convection is realized for the components of an auxiliary velocity on the displaced grids. On the step of diffusion a transition to the new input functions is used. Such approach allows to eliminate the pressure gradient calculation and to guarantee the properties of solenoidality of the velocity vector. The method is tested with the help of the well-known problem of convection in a cavity with a heating from one side.

Keywords: convection, methods of splitting, curved boundary.