A Fast and Efficient Method for Predicting Fluid Flow and Heat Transfer Problems

Abstract

A fast and efficient method based on the proper orthogonal decomposition (POD) technique for predicting fluid flow and heat transfer problems is proposed in this paper. POD is first applied to an ensemble of numerical simulation results at design parameters to obtain the empirical coefficients and eigenfunctions, and then the fluid and temperature fields in the range of design parameters are resolved by a linear combination of empirical coefficients and eigenfunctions. The empirical coefficients at off-design parameters are obtained by a cubic spline interpolation method for steady problems and a Galerkin projection method for transient problems. Finally, the efficiency and accuracy of the algorithm are examined by three examples. The POD based algorithm can predict both the velocity and temperature fields in the range of design parameters accurately at a price of a large number of precomputed cases (snapshots). It also brings significant computational time savings for the new cases within the parameter range presimulated compared with the finite volume method with SIMPLE-like algorithm.