A numerical algorithm for simulation of two-component flows in the Earth's mantle (Q2760700)

In the framework of the model of a two-component isothermal viscous fluid, the authors study numerically slow convective flows in the Earth's mantle with characteristic scale \(1\) cm/year. Attention is focused on the construction of a numerical algorithm for solving the system of equations of the motion of a two-component high viscous fluid written in terms of stream function and vortex variables. A particular attention is paid to describing the difference method for solving a boundary value problem for the system obtained. The difference approximation for the Poisson equation is reduced to solving a system of linear algebraic equations with block three-diagonal matrix of coefficients. To solve the system, the authors apply the direct method based on using orthogonal reflection transformations. To construct the difference scheme for the equation of mass transport for the concentration of a mixture, the authors use the Gauss-Ostrogradskij theorem. The sequence of numerical representations of the resultant finite-difference problem is exposed as an algorithm. The rest of the article is devoted to numerical experiments.