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

Maciej Balajewicz, Irina Tezaur, Earl Dowell

Research output: Contribution to journalArticle

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. 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.

Original languageEnglish (US)
Pages (from-to)224-241
Number of pages18
JournalJournal of Computational Physics
Volume321
DOIs
StatePublished - Sep 15 2016

Keywords

  • Compressible flow
  • Projection-based reduced order model (ROM)
  • Proper Orthogonal Decomposition (POD)
  • Stabilization
  • Stiefel manifold
  • Trace minimization

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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