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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:321

Article

Balajewicz, Maciej¹  Tezaur, Irina²  Dowell, Earl³ 

[1] Univ Illinois, Dept Aerosp Engn, Urbana, IL 61801 USA

[2] Sandia Natl Labs, Quantitat Modeling & Anal Dept, POB 969,MS 9159, Livermore, CA USA

[3] Duke Univ, Dept Mech Engn & Mat Sci, Durham, NC USA

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

DOI  :  10.1016/j.jcp.2016.05.037

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free