A Proper Orthogonal Decomposition Analysis Method for Multimedia Heat Conduction Problems

In this paper, a new proper orthogonal decomposition (POD) analysis method is proposed for numerical analysis of thermal mechanical engineering problems consisting of multiple media. After the creation of a heat conduction solution database for each medium, the “snapshot” approach of the POD technique is applied to facilitate reduced-order modeling (ROM) of the unsteady heat conduction behavior. The snapshot matrix is constructed medium by medium by collecting individual medium solutions at different instances in time through a columnwise manner. By means of expressing physical variables in terms of reduced modes at the individual medium level, a system of differential equations with respect to time is formed by utilizing the consistency conditions of the physical variables on interface boundaries. The solutions of the problem can be obtained by solving the system of equations at different time stops. Two numerical examples are given to demonstrate the efficiency of the proposed method.