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A Galerkin-free model reduction approach for the Navier–Stokes equations

Shinde, Vilas and Longatte, Elisabeth and Baj, Franck and Hoarau, Yannick and Braza, Marianna A Galerkin-free model reduction approach for the Navier–Stokes equations. (2015) Journal of Computational Physics, 309. 148-163. ISSN 0021-9991

(Document in English)

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Official URL: http://dx.doi.org/10.1016/j.jcp.2015.12.051


Galerkin projection of the Navier–Stokes equations on Proper Orthogonal Decomposition (POD) basis is predominantly used for model reduction in fluid dynamics. The robustness for changing operating conditions, numerical stability in long-term transient behavior and the pressure-term consideration are generally the main concerns of the Galerkin Reduced-Order Models (ROM). In this article, we present a novel procedure to construct an off-reference solution state by using an interpolated POD reduced basis. A linear interpolation of the POD reduced basis is performed by using two reference solution states. The POD basis functions are optimal in capturing the averaged flow energy. The energy dominant POD modes and corresponding base flow are interpolated according to the change in operating parameter. The solution state is readily built without performing the Galerkin projection of the Navier–Stokes equations on the reduced POD space modes as well as the following time-integration of the resulted Ordinary Differential Equations (ODE) to obtain the POD time coefficients. The proposed interpolation based approach is thus immune from the numerical issues associated with a standard POD-Galerkin ROM. In addition, a posteriori error estimate and a stability analysis of the obtained ROM solution are formulated. A detailed case study of the flow past a cylinder at low Reynolds numbers is considered for the demonstration of proposed method. The ROM results show good agreement with the high fidelity numerical flow simulation.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at http://www.sciencedirect.com/science/article/pii/S0021999115008700
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Commissariat à l'Energie Atomique et aux énergies alternatives - CEA (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > EDF (FRANCE)
Other partners > Ecole Nationale du Génie de l'Eau et de l'Environnement de Strasbourg - ENGEES (FRANCE)
Other partners > Ecole Nationale Supérieure de Techniques Avancées - ENSTA (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Institut National des Sciences Appliquées de Strasbourg - INSA (FRANCE)
Other partners > Université de Strasbourg - UNISTRA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Laboratory name:
Deposited On:25 May 2016 08:18

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