Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations
Abstract
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.
- Authors:
-
[1];
- Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Duke Univ., Durham, NC (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1333869
- Report Number(s):
- SAND-2015-3378J
Journal ID: ISSN 0021-9991; PII: S0021999116301826
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 321; Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; projection-based reduced order model (ROM); Proper Orthogonal Decomposition (POD); compressible flow; stabilization; trace minimization; Stiefel manifold
Citation Formats
Balajewicz, Maciej, Tezaur, Irina, and Dowell, Earl. Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations. United States: N. p., 2016.
Web. doi:10.1016/j.jcp.2016.05.037.
Balajewicz, Maciej, Tezaur, Irina, & Dowell, Earl. Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations. United States. https://doi.org/10.1016/j.jcp.2016.05.037
Balajewicz, Maciej, Tezaur, Irina, and Dowell, Earl. Wed .
"Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations". United States. https://doi.org/10.1016/j.jcp.2016.05.037. https://www.osti.gov/servlets/purl/1333869.
@article{osti_1333869,
title = {Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations},
author = {Balajewicz, Maciej and Tezaur, Irina and Dowell, Earl},
abstractNote = {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.},
doi = {10.1016/j.jcp.2016.05.037},
journal = {Journal of Computational Physics},
number = C,
volume = 321,
place = {United States},
year = {Wed May 25 00:00:00 EDT 2016},
month = {Wed May 25 00:00:00 EDT 2016}
}
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