A FE-based algorithm for the inverse natural convection problem

Authors

  • J. C.-F. Wong,

    Corresponding author
    1. Department of Mathematics, Room 220, Lady Shaw Building, The Chinese University of Hong Kong, Shatin, Hong Kong
    • Department of Mathematics, Room 220, Lady Shaw Building, The Chinese University of Hong Kong, Shatin, Hong Kong
    Search for more papers by this author
  • P. Yuan

    1. Department of Hydrology and Water Resource Conservancy Engineering, SiChuan University, ChengDu, SiChuan, People's Republic of China
    Search for more papers by this author

Abstract

Several numerical algorithms for solving inverse natural convection problems are revisited and studied. Our aim is to identify the unknown strength of a time-varying heat source via a set of coupled nonlinear partial differential equations obtained by the so-called finite element consistent splitting scheme (CSS) in order to get a good approximation of the unknown heat source from both the measured data and model results, by minimizing a functional that measures discrepancies between model and measured data. Viewed as an optimization problem, the solutions are obtained by means of the conjugate gradient method. A second-order CSS in time involving the direct problem, the adjoint problem, the sensitivity problem and a system of sensitivity functions is used in order to enhance the numerical accuracy obtained for the unknown heat source function. A spatial discretization of all field equations is implemented using equal-order and mixed finite element methods. Numerical experiments validate the proposed optimization algorithms that are in good agreement with the existing results. Copyright © 2010 John Wiley & Sons, Ltd.

Ancillary