期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 258, 期 -, 页码 61-76出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2013.05.004
关键词
Uncertainty quantification; Statistical modeling of nonlinear energy fluxes; Limitations of reduced-order models; Blended stochastic methods; Gaussian closure; Dynamical orthogonality
资金
- NFS [DMS-0456713]
- NSF CMG [DMS-1025468]
- ONR [ONR-DRI N00014-10-1-0554, N00014-11-1-0306]
Order-reduction schemes have been used successfully for the analysis and simplification of high-dimensional systems exhibiting low-dimensional dynamics. In this work, we first focus on presenting generic limitations of order-reduction techniques in systems with stable mean state that exhibit irreducible high-dimensional features such as non-normal dynamics, wide energy spectra, or strong energy cascades between modes. The reduced-order framework that we consider to illustrate these limitations is the dynamically orthogonal (DO) field equations. This framework is applied to a series of examples with stable mean state, including a linear non-normal system, and a nonlinear triad system in various dynamical configurations. After illustrating the weaknesses and generic limitations of order reduction, we develop a novel, two-way coupled, blended approach based on the quasilinear Gaussian (QG) closure and the DO field equations. The new method (QG-DO) overcomes the limitations of its two ingredients and achieves exceptional performance in the examples described previously as well as in other configurations with strongly transient character without using any tuned or adjustable parameters. (c) 2013 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据