proper orthogonal decomposition, temperature field extrapolation, non-periodic boundary conditions, Technology, Engineering (General). Civil engineering (General), TA1-2040, Biology (General), QH301-705.5, Physics, QC1-999, Chemistry, QD1-999

The rapid and accurate prediction of temperature fields in complex structures remains a significant challenge in thermal engineering. Experimental approaches often struggle to provide comprehensive data, while traditional full-order numerical methods are hindered by their excessive computational demands. This study addresses these limitations by developing a novel reduced-order extrapolation method that integrates proper orthogonal decomposition (POD) with the finite volume method (FVM). We demonstrate the efficacy of our approach through its application to multilayered thermally unstable structures under non-periodic boundary conditions. The results reveal exceptional performance in both prediction accuracy and computational efficiency. When validated against experimental data and conventional FVM results, our method achieves a maximum relative error of less than 5% while delivering a remarkable computational speed-up of more than 1400 times when running complex explosive structure simulations. Notably, our analysis uncovers a critical limitation of POD: increasing the number of modes does not proportionally enhance the prediction accuracy, due to inherent methodological constraints. This innovative strategy offers promising potential for real-time temperature monitoring and thermal protection in advanced engineering systems, particularly for complex devices requiring precise thermal management.