A FE-based algorithm for the inverse natural convection problem

• Published in: International journal for numerical methods in fluids Vol. 68; no. 1; pp. 48 - 82
• Main Authors: Wong, J. C.-F., Yuan, P.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 10.01.2012; Wiley
• Subjects: adjoint variable method; Computational methods in fluid dynamics; conjugate gradient method; consistent splitting method; Convection and heat transfer; direct differentiation method; equal-order/mixed finite elements; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); inverse natural convection problem; Physics; Turbulent flows, convection, and heat transfer; Computational fluid dynamics; Digital simulation; Natural convection; Conjugate gradient methods; inverse natural convection problem; consistent splitting method; Finite element method; Inverse problems; adjoint variable method; direct differentiation method; Modelling; equal-order/mixed finite elements; conjugate gradient method; Heat transfer
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.2494

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.