Study on Heat Conduction Model Based on POD Reduced-order Extrapolating Finite Difference Algorithm
Aiming at one-dimensional heat conduction problem,based on singular value decomposition(SVD)and proper projection decomposition(POD)method,a reduced-dimension extrapolation simulation model with few de-grees of freedom and high accuracy is established by extracting characteristic modes.Which gives the mathematical derivation,algorithm process and error analysis of the approximate solution component of model dimension reduc-tion,and realizes the rapid calculation of temperature field.Finally,a numerical example is given to compare the cal-culated results of POD with those of finite difference method(FDM).Results show that the POD method can cap-ture accurate information about the heat transfer process under different time steps,spatial steps,and solution condi-tions.The average calculation speed is 200 times faster than the traditional finite difference method,effectively short-ening the computer simulation time.It assesses the accuracy of low order models and demonstrates that low order e-quations can qualitatively reflect the heat transfer characteristics of the original high-dimensional system.Meanwhile,the maximum relative error between the results obtained from POD and FDM is 0.15%,which meets the accuracy requirements of engineering calculations,we proposed POD dimensionality reduction extrapolation method not only expands the POD feature space,but also gradually improves the numerical solution steps,making up for the short-comings of the POD method,which also verifies the feasibility and effectiveness by using the POD dimensionality re-duction algorithm to study heat transfer problems.The proposed methods and conclusions have certain theoretical reference value for achieving efficient and accurate analysis and numerical simulation of complex heat transfer models in this article.
heat conductionsingular value decompositionreduced-order extrapolatingfinite differencebasis func-tion
NETL
NSTL
万方数据
维普
