Proper orthogonal decomposition with SUPG-stabilized isogeometric analysis for reduced order modelling of unsteady convection-dominated convection-diffusion-reaction problems

• Published in: Journal of computational physics 2019-06, Vol.387, p.280-302
• Main Authors: Li, Richen, Wu, Qingbiao, Zhu, Shengfeng
• Format: Article
• Language: English
• Subjects: Basis functions; Computational physics; Convection-diffusion-reaction; Decomposition reactions; Discretization; Finite element method; Galerkin method; Isogeometric analysis; Mathematical models; Mesh generation; Proper Orthogonal Decomposition; Reduced order modelling; Reduced order models; Stabilization; SUPG
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.02.051

We consider reduced order modelling of unsteady convection-dominated convection-diffusion-reaction problems with proper orthogonal decomposition (POD) in combination with isogeometric analysis. Isogeometric analysis has potential advantages in exact geometry representations, efficient mesh generation, different (h, p, and k) refinements and smooth Bspline/NURBS basis functions. In order to compensate the oscillations caused by the convection-dominated effect, the streamline-upwind Petrov-Galerkin (SUPG) stabilization method is used both in generation of snapshots and POD-Galerkin method. Based on the recent novel and promising discretization method-Isogeometric analysis, we propose a new fully discrete SUPG-stabilized scheme, the associated numerical error features three components due to spatial discretization by isogeometric analysis with SUPG stabilization, time discretization with the Crank-Nicolson scheme, and modes truncation by POD. We show a priori error estimates of the fully discrete scheme and give suitable stabilization parameters numerically. A variety of two and three-dimensional benchmark tests and numerical examples are provided to show the effectiveness, accuracy, and efficiency of the reduced order modelling methods by virtue of potential advantages of isogeometric analysis. •We consider reduced order modelling of unsteady convection-dominated convection-diffusion-reaction problems.•POD is combined with IGA for model order reduction.•SUPG stabilization is used in both offline and online.•A priori error estimates of the fully discrete scheme are given.•Various numerical examples and benchmark tests are presented on single/multi-patch domains in 2D/3D.