A cure for instabilities due to advection-dominance in POD solution to\n advection-diffusion-reaction equations

Abstract

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