Direct and inverse problems of high-viscosity fluid dynamics

Methods and algorithms of numerical simulation for three-dimensional thermal-convective motions of the inhomogeneous high-viscosity incompressible fluid in the direct and inverse time are described. In contrast to the direct-time problem, the inverse-time problem is ill-posed; to solve it, one of the variants of the quasi-reversibility method is used. The main attention is focused on the organization of effective computing processes on parallel-action computers. As an example, simulation results of the inverse problem of restoration of development history of thermal mantle plumes are given.