Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations


Journal Article

© 2016 Elsevier Inc. For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier-Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and the Navier-Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. The reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.

Full Text

Duke Authors

Cited Authors

  • Balajewicz, M; Tezaur, I; Dowell, E

Published Date

  • September 15, 2016

Published In

Volume / Issue

  • 321 /

Start / End Page

  • 224 - 241

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1016/

Citation Source

  • Scopus