Exact analytical solutions of the Stokes equation for testing the equations of mantle convection with a variable viscosity

Presently, the study of the mantle flow structure is mainly based on numerical modeling. The most important stage of the development of a computer program is its testing. For this purpose, results of various test models of convection flows with a given set of parameters are compared. The solution of the Stokes equation, involving the derivative of viscous stresses, is most difficult. Exact analytical solutions of the Stokes equation are obtained in this work for various cases of special loads. These solutions can be used as benchmarks for testing programs of numerical calculation of viscous flows in both geophysics and engineering. The advantage of this testing technique is the exceptional simplicity of the solution form, the admissibility of any spatial viscosity variations, and the fact that solutions can be compared not for a narrow set of the solution parameters but for any distributions of velocities, viscous stresses, and pressures at all points of the space.