An efficient Karhunen-Loève Galerkin method for sequential solution of inverse problems

A practical method is developed to solve inverse natural convection problems sequentially. The sequential algorithm is based on the Kalman filtering technique. By reducing the Boussinesq equation to a reduced order model through the Karhunen-Loève Galerkin procedure, the computational difficulties associated with the covariance equation are overcome. Although this method is found to yield accurate results with efficiency, its accuracy depends on that of the reduced order model employed. In the present investigation, it is demonstrated that this method can be further developed to be reasonably accurate and computationally feasible even with a relatively inaccurate reduced order model by employing the Boussinesq equation as the state equation while adopting the Kalman filter constructed from less accurate reduced order model.