Reduction of modes for the solution of inverse natural convection problems
The authors consider an inverse convection problem of determining the wall heat flux from the temperature measurement within the flow. The unknown heat flux is at the bottom wall of a two-dimensional cavity. The performance function, which is the sum of squared residuals between calculated and observed temperature, is minimized by using the conjugate gradient method. The authors use a Karhunen-Loève-Galerkin method which is a type of Galerkin method that employs the empirical eigenfunctions of Karhunen-Loève decomposition as basis functions. This allows to reduce the governing nonlinear partial differential equations to the minimal number of ordinary differential equations by limiting the solution space to the smallest linear subspace that is sufficient to describe the observed phenomena. This reduction is important, because the techniques for inverse problems are basically iterative, and otherwise the solution of the present inverse natural convection problem requires repeated numerical solutions of Boussinesq equation and its adjoint equation, which is daunting even with the modern high-speed computers.
scientific article; zbMATH DE number 1563789