Fast algorithm for prediction of fluid flow and heat transfer

A fast and efficient algorithm based on the proper orthogonal decomposition (POD) technique for predicting heat transfer and fluid flow was proposed. The POD technique was applied to a set of numerical simulation results to obtain the eigenfunctions that represent the dynamics of the physical problem. The function space considered in the physical problem was limited to the smallest linear subspace when employing these eigenfunctions as basis functions. Instead of projecting the governing equations onto these eigenfunctions, the spectral coefficients were obtained with a simple cubic spline interpolation procedure. The presented algorithm was verified with an example of natural convection in a two dimensional concentric cylinder with a radius ratio of 2.6, and the Rayleigh number varying from 5000 to 1 × 10⁵. The results show that this algorithm can predict the flow and temperature fields with a relative error of 0.7% compared with the exact numerical results. Moreover, it is more than 100 times faster than the SIMPLE algorithm.