Iterative Algorithm for Solving the Retrospective Problem of Thermal Convection in a Viscous Fluid

作者：Tsepelev I A

来源：Fluid Dynamics, 2011, 46(5): 835-842.

DOI：10.1134/S0015462811050164

• Stokes equation
• retrospective problems
• viscous flows
• finite volume method
• ill-posed problems
• natural thermal convection
• incompressible fluid
• packages of engineering programs

A retrospective problem consisting in the reconstruction of an apriori unknown initial state of a highly viscous, incompressible fluid from its known final state is studied. The fluid dynamics model in the Boussinesq approximation is described by the equations of Stokes, incompressibility, and thermal balance with the corresponding initial and boundary conditions. The problem is solved in the inverse direction of time using a new, specially developed iterative method which makes it possible to reduce the original unstable problem to a set of stable problems. The algorithm based on this method is realized on a parallel computer using the OpenFOAM package for engineering calculations. The computational efficiency of the algorithm is analyzed.

• 出版日期2011-10