Numerical Analysis of Transient State Heat Transfer by Spectral Method Based on POD Reduced-Order Extrapolation Algorithm

Abstract

In order to meet the requirements of high accuracy and fast algorithm for numerical heat transfer simulation, an iterative scheme of Proper Orthogonal Decomposition (for short, POD) dimension reduction based on the classical central difference Galerkin spectral method is proposed for solving two-dimensional transient heat conduction problems. The POD dimension reduction spectral method model is constructed by taking the calculation results of classical central difference Galerkin spectral method as sample data. The numerical algorithm characteristics of flow and heat transfer are studied by using a partial differential equation as a mathematical model, and the error estimation is given. Finally, different time intervals are used as parameters to simulate experiments. The results show that the POD method is applicable to transient nonlinear heat conduction problems, and the maximum average relative error of the reconstructed temperature field is 0.89675%. Moreover, the POD method not only has a high calculation accuracy, but also has an average calculation speed as high as 310.25 times that of the central difference Galerkin algorithm. It can be seen that under the condition that the error between the solution of POD dimension reduction extrapolation algorithm and the solution of classical central difference Galerkin spectrum method is small enough, the POD method can greatly reduce the calculation amount, shorten the running time, and ensure a high accuracy of the calculation results, thus verifying the effectiveness and feasibility of the algorithm.

On the Hard Boundary Constraint Method for Fluid Flow Prediction based on the Physics-Informed Neural Network

“…However, constructing such types of models requires additional overhead of data simulation, which could become expensive and even unaffordable for high-dimensional problems. As for projection-based models, an orthogonal linear transformation is first defined from physical coordinates into a modal basis in an unsupervised manner by means of principle orthogonal decomposition (POD) or other methods, and then the PDE operator is projected onto the subspace spanned by the reduced modal basis [11,12]. Although the degree of freedom of solution can be significantly reduced, projected-based models need modifications of the original CFD codes, and the issues of stability and robustness are still not well addressed.…”