The Karhunen–Loève Galerkin method for the inverse natural convection problems

Abstract

The Karhunen–Loève Galerkin method, which is a type of Galerkin method that employs the empirical eigenfunctions of the Karhunen–Loève decomposition as basis functions, is shown to solve inverse natural convection problems efficiently. The specific problem investigated is the inverse natural convection problem of determining the time-varying strength of a heat source from temperature measurement in the domain. The Karhunen–Loève Galerkin procedure can reduce the Boussinesq equation to a set of minimal number of ordinary differential equations by limiting the solution space to the smallest linear subspace that is sufficient to describe the observed phenomena. The performance of the present technique of inverse analysis using the Karhunen–Loève Galerkin procedure is assessed in comparison with the traditional technique of employing the Boussinesq equation, and is found to be very accurate as well as efficient.