By now a substantial body of literature has evolved which deals with the numerical simulation of the 3D convective currents in the Earth’s mantle (see, e.g., [1–4] and references therein). A crucial point is to estimate the reliability of numerical experimental results because the similarity principle fails when the dynamical processes that occur in the Earth’s interior under the known physical parameters of the Earth’s matter are simulated on the laboratory scale. Paper  is especially important for testing numerical models, because it contains results of the 3D simulation of convective currents in the mantle obtained by different authors dealing with model problems.
In solving the 3D problems of hydrodynamics, the variables vorticity and the vector potential appeared to be very useful . Analysis of the known publications shows that these variables receive little attention in the numerical simulation of convective processes in the Earth’s mantle. The present paper is an attempt to construct and test a numerical model of convective processes in the Earth’s mantle using the above variables and the method of fractional steps .