Reduced order model analysis method via proper orthogonal decomposition for transient heat conduction

Abstract

This paper presents a reduced order analysis method for transient heat conduction problems with time-varying boundary conditions by using the proper orthogonal decomposition (POD) modes obtained from the results of using constant boundary conditions. This method can perform interpolation and extrapolation analysis for temperature field at unknown times. First, POD modes are developed by calculating eigenvectors of an autocorrelation matrix composed of snapshots which are clustered by the given results obtained from experiments, finite element method (FEM) or other numerical methods for transient heat transfer problem with constant boundary conditions. Then, the reduced order modeling (ROM) for problems with time-varying boundary condition is obtained by projecting the finite element discrete format on reduced POD modes determined by eigen-value error analysis of the original POD modes. One feature is that the POD modes need not to be reformed when the boundary conditions are time-varying, and one can use a few modes to capture as much as 99% of energy of the whole order model. Examples show that the method developed in this paper is correct and effective. The same POD modes can accurately analyze transient heat conduction problems with the same geometric domain but variety of smooth and time-varying boundary conditions. The method has a good prospect in aero-thermodynamics analysis that needs real-time control or fast calculation.