Stable Galerkin reduced order models for linearized compressible flow

Authors:
Matthew F. Barone;Irina Kalashnikova;Daniel J. Segalman;Heidi K. Thornquist
Affiliations:
Wind Energy Technology Department, Sandia National Laboratories, P.O. Box 5800, MS 1124, Albuquerque, NM 87185-1124, United States;Aerosciences Department, Sandia National Laboratories, P.O. Box 5800, MS 0825, Albuquerque, NM 87185-0825, United States and Institute for Computational and Mathematical Engineering, Stanford Univ ...;Strategic Initiatives Department, Sandia National Laboratories, P.O. Box 5800, MS 0557, Albuquerque, NM 87185-0557, United States;Electrical and Microsystem Modeling Department, Sandia National Laboratories, P.O. Box 5800, MS 0316, Albuquerque, NM 87185-0316, United States
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

The Galerkin projection procedure for construction of reduced order models of compressible flow is examined as an alternative discretization of the governing differential equations. The numerical stability of Galerkin models is shown to depend on the choice of inner product for the projection. For the linearized Euler equations, a symmetry transformation leads to a stable formulation for the inner product. Boundary conditions for compressible flow that preserve stability of the reduced order model are constructed. Preservation of stability for the discrete implementation of the Galerkin projection is made possible using a piecewise-smooth finite element basis. Stability of the reduced order model using this approach is demonstrated on several model problems, where a suitable approximation basis is generated using proper orthogonal decomposition of a transient computational fluid dynamics simulation.