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

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. As a result, 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.
ORCiD logo [1] ;  [2] ;  [3]
  1. Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  3. Duke Univ., Durham, NC (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 0021-9991; PII: S0021999116301826
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 321; Journal Issue: C; Journal ID: ISSN 0021-9991
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; projection-based reduced order model (ROM); Proper Orthogonal Decomposition (POD); compressible flow; stabilization; trace minimization; Stiefel manifold
OSTI Identifier: