期刊
APPLIED MECHANICS REVIEWS
卷 75, 期 3, 页码 -出版社
ASME
DOI: 10.1115/1.4056808
关键词
Krylov methods; Newton-Krylov; periodic orbits; Floquet theory; global stability; laminar-turbulent transition
类别
In fluid dynamics, predicting and characterizing bifurcations, from the onset of unsteadiness to the transition to turbulence, is crucial. This review presents a concise theoretical and numerical framework for computing and analyzing stability of high-dimensional systems. The methods discussed are implemented in an open-source toolbox, nekStab, and their accuracy and performance are demonstrated using standard benchmarks.
In fluid dynamics, predicting and characterizing bifurcations, from the onset of unsteadiness to the transition to turbulence, is of critical importance for both academic and industrial applications. Different tools from dynamical systems theory can be used for this purpose. In this review, we present a concise theoretical and numerical framework focusing on practical aspects of the computation and stability analyses of steady and time-periodic solutions, with emphasis on high-dimensional systems such as those arising from the spatial discretization of the Navier-Stokes equations. Using a matrix-free approach based on Krylov methods, we extend the capabilities of the open-source high-performance spectral element-based time-stepper Nek5000. The numerical methods discussed are implemented in nekStab, an open-source and user-friendly add-on toolbox dedicated to the study of stability properties of flows in complex three-dimensional geometries. The performance and accuracy of the methods are illustrated and examined using standard benchmarks from the fluid mechanics literature. Thanks to its flexibility and domain-agnostic nature, the methodology presented in this work can be applied to develop similar toolboxes for other solvers, most importantly outside the field of fluid mechanics.
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