Reduced-order modelling for solving linear and non-linear equations

摘要

In this article, we present some investigations about the solving of transfer equations by reduced-order models (ROM). We introduce a ROM, the a priori reduction (APR), and we present the results obtained for the 2D unsteady convection-diffusion equation and the ID Burgers equation. The APR approach is then compared with the Karhunen-Loeve decomposition and some properties of this method are emphasized. We show that the computation time necessary for solving these transfer equations is reduced, whereas the accuracy is of the same order of magnitude, in comparison with the solution obtained for the full model with classical methods. At last it is noticed that the APR method is an efficient way to correct the long term behavior of low order dynamical systems.