Numerical Analysis of Transient Non-linear 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, a POD reduced-order extrapolation algorithm based on the iterative format of the classical central difference Gakerkin spectral method is proposed for solving two-dimensional transient heat conduction problems. Using the calculation results of classical central difference Gakerkin spectral method as sample data constructs POD reduced-order spectral method model; A study on numerical algorithm characteristics of flow and heat transfer using partial differential equation as mathematical model, and gives the error estimate; Finally, taking different time steps as parameters to conduct experimental simulation in turn. The results show that: the spectral method based on POD reduced-order extrapolation method is at least 253 times faster than the central difference Gakerkin spectral method, and gradually decreases with the interval of variable parameters. The calculation speed of POD reduced-order model and the calculation speed of central difference are both reduced. However, the average relative error between the temperature field reconstructed by POD reduced dimension model and the central difference result is smaller and the calculation accuracy is higher, the maximum value is not more than 0.11%.The average computational efficiency is 458 times higher than that of the traditional central difference Gakerkin spectral method.