Reduced order modeling with the proper orthogonal decomposition

The POD technique is applied to a set of numerical simulation results to obtain the eigenfunctions that represent the dynamics of the physical problem. The function space is limited to the smallest linear subspace when employing these eigenfunctions as basis functions. The reduced order model is was obtained by projecting the governing equations onto these eigenfunctions. The present algorithm is demonstrated to produce very accurate temperature fields when compared with the exact numerical results, and it is more than 100 times faster than the FVM.