A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
Language
EN
Article de revue
This item was published in
Journal of Computational Physics. 2020-10-01, vol. 425, p. 109916
English Abstract
In this paper, we propose to improve the stabilized POD-ROM introduced in [48] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we propose a three-stage ...Read more >
In this paper, we propose to improve the stabilized POD-ROM introduced in [48] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we propose a three-stage stabilizing strategy that will be very useful when considering very low diffusion coefficients, i.e. in the strongly advection-dominated regime. This approach mainly consists in three ingredients: (1) the addition of a “streamline diffusion” stabilization term to the governing projected equations, (2) the modification of the correlation matrix defining the POD modes associated to the advection stabilization term, and (3) an a-posteriori stabilization scheme. Numerical studies are performed to discuss the accuracy and performance of the new method in handling strongly advection-dominated cases.Read less <
English Keywords
Finite element method
Filtered advection stabilization
A-posteriori stabilization
Proper orthogonal decomposition
Reduced order models
Convection-dominated flows
ANR Project
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003