Karhunen Loeve Galerkin Procedure Research Articles

Stabilization of Rayleigh–Bénard convection by means of mode reduction

A method is developed to suppress the intensity of the Rayleigh–Benard convection by adjusting the heat flux distribution at the bottom boundary under the constraint of constant heat input to the system. The appropriate profile of heat flux, which is changing continually in accordance with the shape of convection cells in the domain, is determined by the model predictive control. The optimal control strategy given by the model predictive control is implemented efficiently by employing the Karhunen–Loeve Galerkin procedure through which the Boussinesq equation is reduced to a low–dimensional dynamic model. This method is found to yield accurate results with a decent requirement of computer time.

Recursive solution of inverse natural convection problems by means of mode reduction

A recursive method based on the Kalman filtering is developed to solve inverse natural convection problems of estimating the unsteady nonuniform wall heat flux from temperature measurements in the flow. By employing the Karhunen–Loeve Galerkin procedure that reduces the Boussinesq equation to a small set of ordinary differential equations, the computational difficulties associated with the Kalman filtering for the partial differential equations are overcome. The present method is assessed through several numerical experiments, and is found to yield satisfactory results.

Solution of an inverse heat transfer problem by means of empirical reduction of modes

An efficent method of solving the inverse heat transfer problem of estimating the unknown function of wall heat flux for laminar flow inside a duct is proposed in the present paper. It is based on the Karhunen—Loeve Galerkin procedure which employs the empirical eigenfunctions of the Karhunen—Loeve decomposition as basis functions of a Galerkin procedure. With the empirical eigenfunctions, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and thus convert the governing equations to a model with a minimum degree of freedom, resulting in a drastic reduction of computation time without loss of accuracy. The performance of the present technique of inverse analysis using the Karhunen—Loeve Galerkin procedure is evaluated by several numerical experiments, and is found to be very accurate as well as efficient.