Iterative algorithm for solving the retrospective problem of natural thermal convection of a viscous fluid

A retrospective problem consisting in the recovery of a priori unknown initial state of a viscous incompressible fluid on the basis of its known final state is investigated. A fluid dynamics model in the Boussinesq approximation is described by Stokes, incompressibility and thermal balance equations under corresponding initial and boundary conditions. To solve the problem in reverse time, a new iterative approach has been developed in which the unstable initial problem is reduced to a series of stable problems. An algorithm, obtained using the proposed approach, is implemented on the parallel computer in OpenFOAM. The results show the computational efficiency of the developed algorithm.