In fluid dynamics ambit the computational cost for simulations is one of the main obstacles related to the need of accurate solutions for both pressure and velocity fields. Since pressure numerical instabilities are challenges we need to become acquainted with when dealing with Navier-Stokes equations, several different strategies have been developed in order to overtake the problem.

In our work we try to accomplish both results, i.e. computational cost reduction and pressure stabilisation, at the same time, by the use of accurate Model Order Reduction techniques.

In this work we present the details about a new path towards the right solution which does not require a proper stabilisation method, followed by some results obtained by its application. In particular also some comparisons between this architecture and some different other stabilisation techniques will be exposed.