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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:425

Article

Azaiez, Mejdi¹  Rebollo, Tomas Chacon^2,3  Rubino, Samuele^2,3 

[1] CNRS, UMR5295, Lab I2M, Inst Polytech Bordeaux, Paris, France

[2] Univ Seville, Dept EDAN, Seville, Spain

[3] Univ Seville, Dept IMUS, Seville, Spain

关键词: Finite element method;    Filtered advection stabilization;    A-posteriori stabilization;    Proper orthogonal decomposition;    Reduced order models;    Convection-dominated flows;   

DOI  :  10.1016/j.jcp.2020.109916

来源: Elsevier

【 摘 要 】

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 advectiondominated 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. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free