Advection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

@INPROCEEDINGS{PacciariniRozza2014a,
author = {Pacciarini, P. and Rozza, G.},
title = {Stabilized reduced basis method for parametrized scalar advection-diffusion
problems at higher {P}\'eclet number: Roles of the boundary layers
and inner fronts},
year = {2014},
pages = {5614--5624},
booktitle = {11th World Congress on Computational Mechanics, WCCM 2014, 5th European
Conference on Computational Mechanics, ECCM 2014 and 6th European
Conference on Computational Fluid Dynamics, ECFD 2014},
}