Iterative algorithm for solving the retrospective problem of natural thermal convection of a viscous fluid
DOI:
https://doi.org/10.7242/1999-6691/2011.4.2.19Keywords:
Stokes equation, retrospective problem, viscous fluid flows, finite volume method, ill-posed problem, natural thermal convection, incompressible flow, engineering software packagesAbstract
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.
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