Reduced order modelling using a POD-based identification method for parametrized PDEs

Gert Van den Eynde, Francesco Belloni, Sabrina Star, Joris Degroote, Jan Vierendeels

Research outputpeer-review


To reduce the computational cost of high-fidelity simulations, model reduction techniques have been developed to approximate parametrized Partial Differential Equations (PDEs) for Computational Fluid Dynamics (CFD) problems. Typically, a Galerkin projection is performed to obtain a reduced order model (ROM). In that case, the governing equations are projected onto the reduced basis space generated by applying a Proper Orthogonal Decomposition (POD) approach on snapshots of the full order simulation. The main issue of this method is its intrusiveness: the construction of the reduced matrices requires access to the full order matrices and thus knowledge of the solvers discretization and solution algorithm. Therefore, a non-intrusive reduced-order method for parametric CFD problems is proposed in this work, which is applicable regardless of the solver. This POD-based identification (PODI) method identifies reduced matrices of the same form as in the POD-Galerkin method using the least-squares technique. This identification uses the set of known time-dependent coefficients obtained by projecting all snapshots on the POD basis in the offline phase. Parameterization of the reduced system requires full order simulations for different parameter values. The resulting reduced system of equations is then solved online for a given set of parameters. The offline-online decomposition of the POD-Galerkin method is thus maintained. To demonstrate the proposed method, numerical results are presented for the convection-diffusion equation, using the finite volume method. The results are compared with the POD-Galerkin method and the benefits and limitations of the presented method are discussed. As the reduced basis is the same for the PODI method and the POD-Galerkin method, also the reduced matrices obtained through respectively identification and projection can be compared.
Original languageEnglish
Title of host publicationProceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
PublisherCIMNE - International Centre for Numerical Methods in Engineering
Number of pages10
ISBN (Print)978-849473116-7
StatePublished - 1 Mar 2020
Event2018 - ECCM6-ECFD7: 6th European Conference on Computational Mechanics - 7th European Conference on Computational Fluid Dynamics - Glasgow
Duration: 11 Jun 201515 Jun 2015


Conference2018 - ECCM6-ECFD7
Country/TerritoryUnited Kingdom

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