2024 , Volume 29, № 2, p.21-34

To describe three-dimensional convection in the Earth’s mantle, a well-known mathematical model is used, which includes the Navier ҫ Stokes equations in the Oberbeck ҫ Boussinesq approximation and the geodynamic approximation. The numerical model of convection in this paper is based on the implicit implementation of the splitting method by physical processes. The velocity ҥeld and the pressure defect on each layer are determined in time by the stationing method. At each layer, it is necessary to integrate the thermal conductivity equation over time. The authors use an implicit scheme of stabilizing correction as an integration scheme. Non-linearity iterations are performed. The constructed numerical model was tested by solving the model problem of convection in a unit cube in a liquid with a nonlinear viscosity corresponding to convection in the Earth’s general mantle [1]. The calculation results are in good agreement with the results of this test. However, in comparison with the previously developed numerical model based on the implicit splitting method with pressure correction, it takes about twice as much computer time to achieve comparable calculation accuracy when using the implicit implementation of the splitting method for physical processes. A test for convection problems in the upper mantle of the Earth is constructed; the results of numerical experiments conҥrming its reliability are presented. The main numerical parameters of the test were chosen similar to the parameters in the well-known international test for general-party convection [1]. The problem was solved using three numerical models based on implicit splitting methods.