The Pseudo-Direct Numerical Simulation Method considered as a Reduced Order Model

The multiscale method called Pseudo-Direct Numerical Simulation (P-DNS) is presented as a Reduced Order Model (ROM) aiming to solve problems obtaining similar accuracy to a solution with many degrees of freedom (DOF). The theoretical basis of P-DNS is other than any standard ROM. However, from a methodological point of view, P-DNS shares the idea of an offline computation, as ROM does, providing the set of coefficients, as a database or table, needed to solve the main problem. This work highlights the advantages and disadvantages of both methodologies. In particular, the drawback of the standard ROM concerning problems where space and time are not separated variables is discussed. The so-called Idelsohn's benchmark is possibly the most elemental test that can be proposed to point out this drawback. This one-dimensional heat transfer problem with a moving heat source shows that, unlike ROMs, P-DNS can solve it by reducing the number of degrees of freedom as much as needed.