The Karhunen-Loeve Galerkin method for the inverse natural convection problems

The Karhunen-Loeve Galerkin method, which is a type of Galerkin method that employs the empirical eigenfunctions of the Karhunen-Loeve decomposition a s basis functions, is shown to solve inverse natural convection problems ef ficiently. The specific problem investigated is the inverse natural convect ion problem of determining the time-varying strength of a heat source from temperature measurement in the domain. The Karhunen-Loeve Galerkin procedur e can reduce the Boussinesq equation to a set of minimal number of ordinary differential equations by limiting the solution space to the smallest line ar subspace that is sufficient to describe the observed phenomena. The perf ormance of the present technique of inverse analysis using the Karhunen-Loe ve Galerkin procedure is assessed in comparison with the traditional techni que of employing the Boussinesq equation, and is found to be very accurate as well as efficient. (C) 2000 Elsevier Science Ltd. All rights reserved.