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Kalashnikova, I.; Arunajatesan, S.;

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A method for constructing stable Proper Orthogonal Decomposition (POD)/Galerkin reduced order models (ROMs) for compressible flow is described. The proposed model reduction technique differs from the approach taken in many applications in that the Galerkin projection step is applied to the continuous system of partial differential equations (PDEs), rather than a semi-discrete representation of these equations. It is demonstrated that the inner product used to define the Galerkin projection is intimately tied to the stability of the resulting model. For linearized conservation laws such as the linearized compressible Euler and linearized compressible Navier-Stokes equations, a symmetry transformation leads to a stable formulation for the inner product. Preservation of stability for the discrete implementation of the Galerkin projection is made possible using piecewise-smooth finite element bases, and a weak enforcement of the boundary conditions. The stability and accuracy of the proposed model reduction approach is studied in the context of two test cases: the problem of an inviscid pressure pulse in a uniform base flow, and a viscous laminar cavity problem. For the second inherently non-linear test case, the non-linear dynamics of the flow are captured in the POD reduced basis modes, but not in the equations projected onto these modes, as the ROM equations are based on a local linearization of the full non-linear flow equations.

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Palavras-chave: Reduced order model (ROM), proper orthogonal decomposition (POD)/Galerkin projection, compressible Navier-Stokes equations, energy method, numerical stability,


DOI: 10.5151/meceng-wccm2012-18407

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Como citar:

Kalashnikova, I.; Arunajatesan, S.; "A STABLE GALERKIN REDUCED ORDER MODEL (ROM) FOR COMPRESSIBLE FLOW", p. 1399-1423 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18407

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