  In this paper, we propose to improve the stabilized POD-ROM introduced by S.
Rubino in [37] to deal with the numerical simulation of advection-dominated
advection-diffusion-reaction equations. In particular, we introduce a
stabilizing post-processing strategy that will be very useful when considering
very low diffusion coefficients, i.e. in the strongly advection-dominated
regime. This strategy is applied both for the offline phase, to produce the
snapshots, and the reduced order method to simulate the new solutions. The new
process of a posteriori stabilization is detailed in a general framework and
applied to advection-diffusion-reaction problems. Numerical studies are
performed to discuss the accuracy and performance of the new method in handling
strongly advection-dominated cases.

Computational Physics;Numerical Analysis;Numerical Analysis