期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 228, 期 6, 页码 1932-1946出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2008.11.015
关键词
Reduced order models; Galerkin projection; Energy method; Linearized Euler equations
资金
- Laboratory Directed Research and Development program at Sandia National Laboratories
- United States Department of Energy's National Nuclear Security Administration [DE-AC0494AL85000]
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. (C) 2008 Elsevier Inc. All rights reserved.
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