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

Mejdi Azaïez (1) , Tomás Chacón , Samuele Rubino

1 I2M - Institut de Mécanique et d'Ingénierie

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.

Mots clés: finite element method; filtered advection stabilization; a-posteriori stabiliza- tion; proper orthogonal decomposition; reduced order models; convection-dominated flows

Domaines: Mathématiques [math]

Mejdi Azaïez, Tomás Chacón, Samuele Rubino. A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations. Journal of Computational Physics, 2021, 425, pp.109916. ⟨10.1016/j.jcp.2020.109916⟩. ⟨hal-03000327⟩